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This study deals with the numerical verifications of the experimentally determined dynamic characteristics of neat Acrylonitrile-Butadiene-Styrene (ABS) thermoplastic as well as hemp fiber particle-added ABS possessing three various weight fractions (1%, 5%, and 10%).To this end, significant dynamic modal parameters including natural frequencies and corresponding mode shapes have been predicted by performing finite element analyses in Abaqus engineering software on the rectangular plates with a dimension of 120x145mm whose one edge is clamped and the remaining ones are completely free. Eigenvalue extraction to estimate the first three natural frequencies and the corresponding mode shapes of the rectangular plates has been achieved by using the Lanczos eigensolver which is regarded as one of the most powerful methods for the solution of large generalized eigenvalue problems. The first three natural frequencies and corresponding mode shapes have been successfully extracted from the finite element analyses. The predicted dynamic modal parameters have been favorably compared to the modal test measurements. Thus, the experimental results have been validated against the numerical predictions., {"references":["Olivera S, Muralidhara HB, Venkatesh K, Gopalakrishna K, Vivek CS. Plating on acrylonitrile–butadiene–styrene (ABS) plastic: a review. J Mater Sci. 2016;51(8):3657– 74","Yousefi M, Gholamian F, Ghanbari D, Salavati-Niasari M. Polymeric nanocomposite materials: Preparation and characterization of star-shaped PbS nanocrystals and their influence on the thermal stability of acrylonitrile-butadiene-styrene (ABS) copolymer. Polyhedron [Internet]. 2011;30(6):1055–60. Available from: http://dx.doi.org/10.1016/j.poly.2011.01.012","Kamelian FS, Saljoughi E, Shojaee Nasirabadi P, Mousavi SM. Modifications and research potentials of acrylonitrile/butadiene/styrene (ABS) membranes: A review. Polym Compos. 2018;39(8):2835–46.","H R M, Benal MGM, G S P, Tambrallimath V, Ramaiah K, Khan TMY, et al. Effect of Short Glass Fiber Addition on Flexural and Impact Behavior of 3D Printed Polymer Composites. ACS Omega [Internet]. 2023 Mar 14;8(10):9212–20. Available from: https://pubs.acs.org/doi/10.1021/acsomega.2c07227","Dhandapani A, Krishnasamy S, Nagarajan R, Selvaraj ADA, Thiagamani SMK, Muthukumar C, et al. Investigation of Wear Behavior in Self-Lubricating ABS Polymer Composites Reinforced with Glass Fiber/ABS and Glass Fiber/Carbon Fiber/ABS Hybrid. Lubricants [Internet]. 2023 Mar 13;11(3):131. Available from: https://www.mdpi.com/2075-4442/11/3/131","Zahid A, Anwar MT, Ahmed A, Raza Y, Gohar GA, Jamshaid M. Synthesis and Investigation of Mechanical Properties of the Acrylonitrile Butadiene Styrene Fiber Composites Using Fused Deposition Modeling. 3D Print Addit Manuf [Internet]. 2023 Jan 30; Available from: https://www.liebertpub.com/doi/10.1089/3dp.2022.0199","Young D, Wetmore N, Czabaj M. Interlayer fracture toughness of additively manufactured unreinforced and carbon-fiber-reinforced acrylonitrile butadiene styrene. Addit Manuf [Internet]. 2018 Aug;22(February):508–15. Available from: https://doi.org/10.1016/j.addma.2018.02.023","Kumar P, Palsule S. Bamboo Fiber Reinforced Chemically Functionalized Acrylonitrile Butadiene Styrene Composites by Palsule Process. J Nat Fibers [Internet]. 2023;20(1). Available from: https://doi.org/10.1080/15440478.2022.2150741","Sahu S, Sahu SBBPJ, Nayak S, Roul MK, Khuntia SK. Effect of chemical treatment and fiber loading on various properties of Bauhinia vahlii bast fibers/acrylonitrile butadiene styrene composites for automotive body parts. Polym Compos [Internet]. 2022 Aug 20;43(8):4909–18. Available from: https://onlinelibrary.wiley.com/doi/10.1002/pc.26751","Chauhan V, Kärki T, Varis J. Effect of Fiber Content and Silane Treatment on the Mechanical Properties of Recycled Acrylonitrile-Butadiene-Styrene Fiber Composites. Chemistry (Easton) [Internet]. 2021 Nov 1;3(4):1258–70. Available from: https://www.mdpi.com/1996-1944/14/9/2223","Rutkowski J V, Levin B. Pyrolysis and Combustion Products and their Toxicity-A Review of the Literature. Fire Mater. 1986;10(July):93–105.","Chotirat L, Chaochanchaikul K, Sombatsompop N. On adhesion mechanisms and interfacial strength in acrylonitrile–butadiene–styrene/wood sawdust composites. Int J Adhes Adhes [Internet]. 2007 Dec;27(8):669–78. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0143749607000309","Threepopnatkul P, Krachang T, Teerawattananon W, Suriyaphaparkorn K, Kulsetthanchalee C. Study of surface treatment of pineapple leaf fiber (PALF) on performance of PALF/ABS composites. ECCM 2012 - Compos Venice, Proc 15th Eur Conf Compos Mater. 2012;(June):24–8.","Akato K, Tran CD, Chen J, Naskar AK. Poly(ethylene oxide)-Assisted Macromolecular Self-Assembly of Lignin in ABS Matrix for Sustainable Composite Applications. ACS Sustain Chem Eng [Internet]. 2015 Dec 7;3(12):3070–6. Available from: https://pubs.acs.org/doi/10.1021/acssuschemeng.5b00509","Obianuju OH. Mechanical Properties, Morphology and Elemental Composition of Composites Produced from Thermoplastic Polymers Filled with Egg Shell. Int Res J Pure Appl Chem [Internet]. 2021 Mar 9;22(1):59–78. Available from: https://www.journalirjpac.com/index.php/IRJPAC/article/view/30374","Ponsuriyaprakash S, Udhayakumar P, Pandiyarajan R. Experimental Investigation of ABS Matrix and Cellulose Fiber Reinforced Polymer Composite Materials. J Nat Fibers [Internet]. 2020 Nov 9;00(00):1–12. Available from: https://www.tandfonline.com/doi/full/10.1080/15440478.2020.1841065","Neher B, Bhuiyan MMR, Kabir H, Gafur MA, Ahmed F. Fabrication and Optical Characterization of Palm Fiber Reinforced Acrylonitrile Butadiene Styrene Based Composites: Band Gap Studies. Mater Sci Appl. 2018;09(02):246–57.","Ewins DJ. Modal Testing: Theory, Practice and Application. 2001;562.","Jinguang Z, Hairu Y, Guozhi C, Zeng Z. Structure and modal analysis of carbon fiber reinforced polymer raft frame. J Low Freq Noise Vib Act Control. 2018;37(3):577–89.","Avitabile P. Modal Testing: A Practitioner's Guide [Internet]. Modal Testing: A Practitioner's Guide. Chichester, UK: John Wiley & Sons Ltd; 2017.","Das P, Sahu SK. Free vibration analysis of industry-driven woven fiber laminated carbon/epoxy composite beams by experimental and numerical approach. Polym Polym Compos. 2021;29(9_suppl):S1371–85.","Ramalho LDC, Sánchez-Arce IJ, Gonçalves DC, Belinha J, Campilho RDSG. Numerical analysis of the dynamic behaviour of adhesive joints: A review. Int J Adhes Adhes. 2022;118(June).","Munteanu M V., Stanciu MD, Nǎstac SM, Savin A. Modal analysis of small turbine blade made from glass fibres composites. IOP Conf Ser Mater Sci Eng. 2018;444(6).","Orlowska A, Graczykowski C, Galezia A. The effect of prestress force magnitude on the natural bending frequencies of the eccentrically prestressed glass fibre reinforced polymer composite beams. J Compos Mater. 2018;52(15):2115–28.","Yin J, Xu L, Wang H, Xie P, Huang S, Liu H, et al. Accurate and fast three-dimensional free vibration analysis of large complex structures using the finite element method. Comput Struct. 2019;221:142–56.","Malatip A, Prasomsuk N, Siriparu C, Paoprasert N, Otarawanna S. An efficient matrix tridiagonalization method for 3D finite element analysis of free vibration. Math Comput Simul [Internet]. 2020;172:90–110. Available from: https://doi.org/10.1016/j.matcom.2019.12.017","Zhao JG, Liu GR, Huo SH, Li ZR. Modes and modal analysis of three-dimensional (3D) structures based on the smoothed finite element methods (S-FEMs) using automatically generatable tetrahedral meshes. Eng Anal Bound Elem. 2022;140(November 2021):262– 81.","Pham CH, Hancock GJ. Numerical simulation of high strength cold-formed purlins in combined bending and shear. J Constr Steel Res [Internet]. 2010;66(10):1205–17. Available from: http://dx.doi.org/10.1016/j.jcsr.2010.04.014","Laím L, Rodrigues JPC, Silva LS Da. Experimental and numerical analysis on the structural behaviour of cold-formed steel beams. Thin-Walled Struct [Internet]. 2013;72:1–13. Available from: http://dx.doi.org/10.1016/j.tws.2013.06.008","Dassault Systèmes. Abaqus Analysis User's Manual 6.12 [Internet]. Documentation. 2012 [cited 2022 Nov 14]. p. 23.3.1 Extended Drucker-Prager models. Available from: http://130.149.89.49:2080/v6.12"]}

A very limited exploratory research has been conducted to elucidate the natural particle addition effects on the dynamic characteristics of polymers including natural frequency, mode shape, and damping ratio. In response to this, the present study has been dedicated to the examination of the effect of added hemp fiber particles on the modal parameters of an industrially important Acrylonitrile-Butadiene-Styrene (ABS) thermoplastic. Biocomposites were fabricated by incorporating hemp particles into ABS at three various weight fractions (1%, 5%, and 10 %). Modal testing aiming to measure the associated dynamic modal parameters was performed on both the rectangular neat ABS and ABS biocomposites with a dimension of 120x145 mm by using a roving impact hammer method with a fixed response measurement point. A one-edge clamped boundary condition was successfully applied to the testing specimens. The modal test results revealed that the incorporation of hemp particles generally enhances the modal parameters of neat ABS such as the first three natural frequencies and associated damping ratios. The experimental results also put forth that the mentioned modal parameters tend to improve considerably with increasing particle content. Regardless of the particle weight fraction, it was found that the incorporation of hemp particles possesses an insignificant influence on the patterns of the first three mode shapes of neat ABS., {"references":["Olivera S, Muralidhara HB, Venkatesh K, Gopalakrishna K, Vivek CS. Plating on acrylonitrile–butadiene–styrene (ABS) plastic: a review. J Mater Sci. 2016;51(8):3657– 74.","Yousefi M, Gholamian F, Ghanbari D, Salavati-Niasari M. Polymeric nanocomposite materials: Preparation and characterization of star-shaped PbS nanocrystals and their influence on the thermal stability of acrylonitrile-butadiene-styrene (ABS) copolymer. Polyhedron [Internet]. 2011;30(6):1055–60. Available from: http://dx.doi.org/10.1016/j.poly.2011.01.012","Kamelian FS, Saljoughi E, Shojaee Nasirabadi P, Mousavi SM. Modifications and research potentials of acrylonitrile/butadiene/styrene (ABS) membranes: A review. Polym Compos. 2018;39(8):2835–46.","H R M, Benal MGM, G S P, Tambrallimath V, Ramaiah K, Khan TMY, et al. Effect of Short Glass Fiber Addition on Flexural and Impact Behavior of 3D Printed Polymer Composites. ACS Omega [Internet]. 2023 Mar 14;8(10):9212–20. Available from: https://pubs.acs.org/doi/10.1021/acsomega.2c07227","Dhandapani A, Krishnasamy S, Nagarajan R, Selvaraj ADA, Thiagamani SMK, Muthukumar C, et al. Investigation of Wear Behavior in Self-Lubricating ABS Polymer Composites Reinforced with Glass Fiber/ABS and Glass Fiber/Carbon Fiber/ABS Hybrid. Lubricants [Internet]. 2023 Mar 13;11(3):131. Available from: https://www.mdpi.com/2075-4442/11/3/131","Zahid A, Anwar MT, Ahmed A, Raza Y, Gohar GA, Jamshaid M. Synthesis and Investigation of Mechanical Properties of the Acrylonitrile Butadiene Styrene Fiber Composites Using Fused Deposition Modeling. 3D Print Addit Manuf [Internet]. 2023 Jan 30; Available from: https://www.liebertpub.com/doi/10.1089/3dp.2022.0199","Young D, Wetmore N, Czabaj M. Interlayer fracture toughness of additively manufactured unreinforced and carbon-fiber-reinforced acrylonitrile butadiene styrene. Addit Manuf [Internet]. 2018 Aug;22(February):508–15. Available from: https://doi.org/10.1016/j.addma.2018.02.023","Kumar P, Palsule S. Bamboo Fiber Reinforced Chemically Functionalized Acrylonitrile Butadiene Styrene Composites by Palsule Process. J Nat Fibers [Internet]. 2023;20(1). Available from: https://doi.org/10.1080/15440478.2022.2150741","Sahu S, Sahu SBBPJ, Nayak S, Roul MK, Khuntia SK. Effect of chemical treatment and fiber loading on various properties of Bauhinia vahlii bast fibers/acrylonitrile butadiene styrene composites for automotive body parts. Polym Compos [Internet]. 2022 Aug 20;43(8):4909–18. Available from: https://onlinelibrary.wiley.com/doi/10.1002/pc.26751","Chauhan V, Kärki T, Varis J. Effect of Fiber Content and Silane Treatment on the Mechanical Properties of Recycled Acrylonitrile-Butadiene-Styrene Fiber Composites. Chemistry (Easton) [Internet]. 2021 Nov 1;3(4):1258–70. Available from: https://www.mdpi.com/1996-1944/14/9/2223","Rutkowski J V, Levin B. Pyrolysis and Combustion Products and their Toxicity-A Review of the Literature. Fire Mater. 1986;10(July):93–105.","Chotirat L, Chaochanchaikul K, Sombatsompop N. On adhesion mechanisms and interfacial strength in acrylonitrile–butadiene–styrene/wood sawdust composites. Int J Adhes Adhes [Internet]. 2007 Dec;27(8):669–78. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0143749607000309","Threepopnatkul P, Krachang T, Teerawattananon W, Suriyaphaparkorn K, Kulsetthanchalee C. Study of surface treatment of pineapple leaf fiber (PALF) on performance of PALF/ABS composites. ECCM 2012 - Compos Venice, Proc 15th Eur Conf Compos Mater. 2012;(June):24–8.","Akato K, Tran CD, Chen J, Naskar AK. Poly(ethylene oxide)-Assisted Macromolecular Self-Assembly of Lignin in ABS Matrix for Sustainable Composite Applications. ACS Sustain Chem Eng [Internet]. 2015 Dec 7;3(12):3070–6. Available from: https://pubs.acs.org/doi/10.1021/acssuschemeng.5b00509","Obianuju OH. Mechanical Properties, Morphology and Elemental Composition of Composites Produced from Thermoplastic Polymers Filled with Egg Shell. Int Res J Pure Appl Chem [Internet]. 2021 Mar 9;22(1):59–78. Available from: https://www.journalirjpac.com/index.php/IRJPAC/article/view/30374","Ponsuriyaprakash S, Udhayakumar P, Pandiyarajan R. Experimental Investigation of ABS Matrix and Cellulose Fiber Reinforced Polymer Composite Materials. J Nat Fibers [Internet]. 2020 Nov 9;00(00):1–12. Available from: https://www.tandfonline.com/doi/full/10.1080/15440478.2020.1841065","Neher B, Bhuiyan MMR, Kabir H, Gafur MA, Ahmed F. Fabrication and Optical Characterization of Palm Fiber Reinforced Acrylonitrile Butadiene Styrene Based Composites: Band Gap Studies. Mater Sci Appl. 2018;09(02):246–57.","Ewins DJ. Modal Testing: Theory, Practice and Application. 2001;562. Available from: http://www.amazon.com/Modal-Testing-Application-Mechanical- Engineering/dp/0863802184","Jinguang Z, Hairu Y, Guozhi C, Zeng Z. Structure and modal analysis of carbon fiber reinforced polymer raft frame. J Low Freq Noise Vib Act Control. 2018;37(3):577–89.","Avitabile P. Modal Testing: A Practitioner's Guide [Internet]. Modal Testing: A Practitioner's Guide. Chichester, UK: John Wiley & Sons Ltd; 2017. Available from: http://doi.wiley.com/10.1002/9781119222989","Das P, Sahu SK. Free vibration analysis of industry-driven woven fiber laminated carbon/epoxy composite beams by experimental and numerical approach. Polym Polym Compos. 2021;29(9_suppl):S1371–85.","Ramalho LDC, Sánchez-Arce IJ, Gonçalves DC, Belinha J, Campilho RDSG. Numerical analysis of the dynamic behaviour of adhesive joints: A review. Int J Adhes Adhes. 2022;118(June).","Munteanu M V., Stanciu MD, Nǎstac SM, Savin A. Modal analysis of small turbine blade made from glass fibres composites. IOP Conf Ser Mater Sci Eng. 2018;444(6).","Orlowska A, Graczykowski C, Galezia A. The effect of prestress force magnitude on the natural bending frequencies of the eccentrically prestressed glass fibre reinforced polymer composite beams. J Compos Mater. 2018;52(15):2115–28.","Yin J, Xu L, Wang H, Xie P, Huang S, Liu H, et al. Accurate and fast three-dimensional free vibration analysis of large complex structures using the finite element method. Comput Struct. 2019;221:142–56.","Malatip A, Prasomsuk N, Siriparu C, Paoprasert N, Otarawanna S. An efficient matrix tridiagonalization method for 3D finite element analysis of free vibration. Math Comput Simul [Internet]. 2020;172:90–110. Available from: https://doi.org/10.1016/j.matcom.2019.12.017","Zhao JG, Liu GR, Huo SH, Li ZR. Modes and modal analysis of three-dimensional (3D) structures based on the smoothed finite element methods (S-FEMs) using automatically generatable tetrahedral meshes. Eng Anal Bound Elem. 2022;140(November 2021):262– 81.","Pham CH, Hancock GJ. Numerical simulation of high strength cold-formed purlins in combined bending and shear. J Constr Steel Res [Internet]. 2010;66(10):1205–17. Available from: http://dx.doi.org/10.1016/j.jcsr.2010.04.014","Laím L, Rodrigues JPC, Silva LS Da. Experimental and numerical analysis on the structural behaviour of cold-formed steel beams. Thin-Walled Struct [Internet]. 2013;72:1–13. Available from: http://dx.doi.org/10.1016/j.tws.2013.06.008","Dassault Systèmes. Abaqus Analysis User's Manual 6.12 [Internet]. Documentation. 2012 [cited 2022 Nov 14]. p. 23.3.1 Extended Drucker-Prager models. Available from: http://130.149.89.49:2080/v6.12"]}

In daily operations, there are lots of blade disk structures operating in water, e.g., hydraulic turbines and pumps, whose dynamic behavior may be severely affected by the added mass effect. Their mode shape change problem from vacuum to water due to the added mass effect has been studied in this paper. The added mass effect of simplified blade disk structures submerged in still water has been studied numerically first in this paper. Acoustic fluid–structure interaction technology has been used to simulate the fluid and structure coupling effect. Through comparing the strain energy percentage of the disk part in water with those in air under different disk material densities, it showed that different parts of the submerged blade disk structures can suffer from different average added mass factors, which makes the modal shapes of some modes with strong blade disk interactions change a lot from vacuum to water, thus produces a large influence on the optimal design of submerged blade disk structures. Based on the conclusions of the simplified model, the situation of a Francis turbine runner model was investigated, and the results fit the conclusions on the simplified model very well.

This paper investigated the static and dynamic behaviors of isotropic cracked simply supported beam using finite element analysis (FEA), ANSYS software. Modal and harmonic vibration analysis of intact and damaged beam were performed in order to extract mode shapes of bending vibration, natural frequencies and obtain frequency response diagram. Static finite element analysis of undamaged and damaged simply supported beam was carried out to determine zero frequency deflection, then stiffness of intact and cracked beam was computed using conventional formula. Crack damage severity of damaged beam was calculated and it is noticed that as crack position is increased from left hand support of beam up to central point and crack depth is increased, then crack damage severity increases. The effect of mode shape pattern is investigated and it is found that the amount of decreasing of natural frequency is proportional to the normalized mode shape at position of crack. The exhibited correlation between results for damaged beam revealed that crack damage severity is proportional to zero frequency deflection and inversely proportional to first mode frequency.

Stability problems are inherent to power systems due to their nonlinear and dynamic nature. Adding to that dynamics is the unavoidable and constant development of power systems to satisfy the increased need for electricity. Furthermore, the rapid progress in the transition to renewable energy, the modernization of power systems and the progress in the technologies involved, certainly adds to the issue. It is clearly evident that we are quickly outgrowing our present power system and its capabilities. The final result is a power system, exploited at its limits, very much susceptible to stability issues. Small-signal stability problems - the topic of interest in this thesis, are observable when one generator, or a group of generators, tend to swing relative to each other. Left unchecked, without adequate countermeasures, these oscillations may increase and further worsen the system stability, potentially ending in a wide system blackout. Offline modal analysis has proven itself as a great approach to study poorly damped oscillations appearing due to small disturbances. Moreover, modal analysis provides important information on the small signal dynamics of the system as a whole. On the other hand, real time mode estimation methods, made possible with the addition of phasor measurement units, are able to estimate the mode of oscillation from actual system measurements, but lack the information abundance which modal analysis offers. The scope of this thesis provides a method utilizing principal components analysis, capable of linking the real time estimated mode with a mode from an offline simulation, consequently adding valuable information to the real time method in question. The key steps of the proposed method are as follows. Principal components analysis is used on a large database of mode shapes, obtained by offline modal analysis of various power system scenarios. Following is the estimation of the mode shape of an actual power system oscillation using spectral analysis. More correctly, the mode shape magnitude and mode shape phase are determined using the power spectral density and the cross power spectral density of the measurements. The obtained mode shape is compared with the database using the calculated principal components from the first step. The objective is to distinguish one or several modes from the database which show similarities with the estimated mode. The method is evaluated on the New England 39 bus test system. Five scenarios are used to create the database. Small-signal disturbances are applied to each scenario to provide the ambient oscillations. The results show that the proposed method is an effective tool in finding similar modes. With only one dominant mode present, it recognizes that the oscillation comes from a scenario in the database where the online simulation is conducted. When analyzing an oscillation where two dominant modes are present, it appears that the method falls short in the same task. However, it manages to provide a set of similar modes on which we can make our educated assumptions and base our further analysis. Težave s stabilnostjo so inherentne za elektroenergetske sisteme zaradi njihove nelinearne in dinamične narave. K tej dinamiki prispeva neizogibni in stalni razvoj elektroenergetskih sistemov, da bi zadovoljili vse večje potrebe po električni energiji. Poleg tega k temu zagotovo prispeva tudi hiter prehod na obnovljive vire energije, modernizacija elektroenergetskih sistemov in vključevanje naprednih tehnologij. S tem pa hitro preraščamo sedanji elektroenergetski sistem in njegove zmogljivosti. Končni rezultat je elektroenergetski sistem, ki je izkoriščen do skrajnih meja in s tem zelo dovzeten za težave s stabilnostjo. Izzivi stabilnosti pri majhnih motnjah, ki so predmet te disertacije, so opazni, kadar generator ali skupina njih niha relativno drug na drugega. Nenadzorjevanje teh nihanj, brez ustreznih protiukrepov, vodi do njihovega povečanja in posledično poslabšanje stabilnosti sistema, kar lahko privede do razpada celotnega sistema. Modalna analiza se je izkazala kot odličen pristop za preučevanje slabo dušenih nihanj, ki se pojavljajo zaradi majhnih motenj. Poleg tega, modalna analiza zagotavlja pomembne informacije o dinamiki v okviru celotnega sistema. Po drugi strani pa, metode ocenjevanja stanja nihanj v realnem času, ki potrebujejo meritve fazorjev, omogočajo oceno nihanja iz dejanskih meritev sistema, vendar z obilico informacij manj kot jih pridobimo z modalno analizo. Obseg te disertacije ponuja metodo, ki uporablja analizo glavnih komponent in lahko poveže analizo v realnem času z simulacijo, kar posledično doda koristne informacije k metodi ocenjevanja stanja nihanj v realnem času. Modalna analiza (analiza v frekvenčni domeni) se že vrsto let uporablja kot orodje za ocenjevanje stabilnosti elektroenergetskih sistemov pri majhnih motnjah. Metoda je povsem matematična in je sestavljena iz linearizacije diferencialnih enačb, ki definirajo elektroenergetski sistem, in reševanja njegovih lastnih vrednosti in lastnih vektorjev (levega, imenovanega vodljivost načina, in desnega, imenovanega spoznavnost načina), ki zagotavljajo obilico informacij o dinamiki sistema. Ena težava pri modalni analizi je povezana z obnašanjem elektroenergetskih sistemov v realnem času. Ker se razmere nenehno spreminjajo, ne moremo domnevati, da matematični model tega sistema ostaja enak. Tako izvedena modalna analiza ne more zajeti dinamike razvijajočega se sistema. Pojav fazorskih merilnih enot je privedel do možnosti ocenjevanja načina v realnem času. Prvič, z obravnavanimi metodami je bilo mogoče oceniti frekvenco in dušenje nihanja, kar je bil velik korak naprej pri ocenjevanju stabilnosti v realnem času. V zadnjem času se poleg realno-časovne ocene frekvence in dušenja načina, veliko zanimanja posveča oceni spoznavnosti načina. Natančna ocena spoznavnosti načina lahko pomaga pri ublažitvi nihanja elektroenergetskega sistema z zagotavljanjem informacij za izvajanje ustreznih nadzornih ukrepov. Poznavanje spoznavnosti načina skupaj s frekvenco in dušenjem nihanj je dobra osnova za oceno stabilnosti za majhne motnje. Ključni koraki predlagane metode v tej disertaciji so naslednji. Analiza glavnih komponent se opravi na veliki bazi podatkov stanja, pridobljenih z modalno analizo za različne scenarije elektroenergetskega sistema. Sledi ocena stanja dejanskega nihanja elektroenergetskega sistema z uporabo spektralne analize. Natančneje, velikost spoznavnosti načina in faza spoznavnosti načina se določita z uporabo spektralne gostote moči in vmesne spektralne gostote moči meritev. Dobljena spoznavnost načina se primerja s podatkovno bazo iz prvega koraka s pomočjo izračunanih glavnih komponent. Cilj je prepoznati enega ali več načinov iz podatkovne baze, ki so podobni dejanskemu sistemu. Metoda je bila preizkušena na 39 vozliščnem preizkusnem sistemu. Podatkovna baza je bila pridobljena iz petih različnih scenarijev sistema. V vsakem scenariju je bila prisotna majhna motnja, da se zagotovi dejanska nihanja. Magistrsko delo pa je organizirano na naslednji način. Najprej predstavimo teoretično ozadje stabilnosti elektroenergetskega sistema. Poudarek je na kotni stabilnosti, in sicer na stabilnosti za majhne motnje in modalni analizi. Začnemo s splošnim fizikalnim ozadjem stabilnosti elektroenergetskega sistema, nato pa se obrnemo na nihajno enačbo, iz katere izpeljemo, kako pride do oscilacij rotorja. Poglavje zaključujemo s tem kako poteka modalna analiza in kako pomaga pri oceni stabilnosti elektroenergetskega sistema. Drugič, predlagamo našo metodo za oceno stabilnosti za majhne motnje in jo razdelimo na dva dela. Prvi prikazuje metodo ocenjevanja spoznavnosti načina, ki temelji na spektralni gostoti moči in vmesne spektralne gostote moči ambientalnih meritev. Zagotavljamo tudi teoretično ozadje spektralne analize in kako nam pomaga, da lahko pridemo do spoznavnosti načina iz ambientalnih meritev. Drugi del je namenjen analizi glavnih komponent. Posredujemo teorijo za analizo glavnih komponent in kako se uporablja kot tehnika zmanjševanja dimenzij. Predstavljamo grafični uporabniški vmesnik narejen v programskem okolju Matlab, ki prikazuje kako se PCA uporablja pri prepoznavanju podobnih načinov iz baze podatkov. Nazadnje izvajamo simulacije na testnem 39 vozliščnem sistemu, iz katerega pridobimo meritve in nadaljujemo s testiranjem veljavnosti metode. Rezultati kažejo, da je predlagana metoda učinkovito orodje za iskanje podobnih nihanj. Ob prisotnosti le enega prevladujočega načina metoda prepozna, da nihanje izvira iz scenarija v podatkovni bazi, kjer se izvaja dejanska analiza. Pri analizi nihanja, kjer sta prisotna dva ali več prevladujočih načinov se zdi, da je metoda pri isti nalogi pomanjkljiva. Kljub temu ji uspe zagotoviti niz podobnih načinov, na podlagi katerih lahko oblikujemo svoje utemeljene domneve in utemeljimo nadaljnjo analizo.

Elastocaloric cooling technology recently attracted significant attention as an environmental friendly alternative to vapor-compression technology. It is based on the elastocaloric effect, which occurs in superelastic shape memory alloys (SMAs) during stress-induced martensitic transformation. To date, several proof-of-concept devices (mostly based on tensile loading) have been developed, but limited fatigue life was shown to be one of the major issues. Compressive loading improves the fatigue life of such devices significantly, but in return buckling of SMA structure might occur. To overcome this challenge, it is crucial to understand the buckling phenomena of SMA structures, especially for thin-walled tubes that seem to be ideal candidates for application in elastocaloric cooling devices. Here, we experimentally investigated the effects of the diameter-to-thickness ratio (D$_{out}$/t) and slenderness (λ) on buckling stability of Ni-Ti tubes that were subjected to cyclic compressive loading. In total, 161 superelastic Ni-Ti tubes with outer diameter (D$_{out}$) ranging from 2 mm to 3 mm, D$_{out}$/t ranging from 5 to 25 and gauge lengths (L$_g$) ranging from 6 to 20 mm were tested. The loading procedure consisted of 3 parts: (I) 1 isothermal full-transformation loading cycle, (II) 50 training cycles, and (III) 20 adiabatic cycles to simulate loading conditions in elastocaloric device. We constructed experimental phase diagrams of buckling modes in λ – D$_{out}$/t space for constant D$_{out}$ and in λ – D$_{out}$ space for constant D$_{out}$/t ratio. Marked areas of functionally stable tubes in these phase diagrams give the design guidance for future developments of durable and efficient elastocaloric devices and other applications, e.g. actuators and dampers.

Damage occurrence is always inevitable in structures. So far, many examples of damage types in engineering structures have been recorded with many losses of human and financial. For this reason, the detecting of structural damages during its exploitation to provide safety with the lowest cost has been the subject of many researchers in the last two decades. In this regard, the wavelet transform is a powerful mathematical tool for signal processing, has attracted the attention of many researchers in the field of health monitoring of structures. In this paper, due to the increase of steel plate shear wall in the building industry, it was considered the problem of detecting the location of the damage in steel plates. In this paper, due to the increase of steel plate shear wall in the building industry, it was considered the problem of detecting the location of the damage in steel plates. At first, the steel plate was modeled in ABAQUS finite element software with free support conditions, and then the healthy and damaged first eight mode shape was extracted. The primary and secondary modes shape was analyzed using discrete two-dimensional wavelet transform as a two-dimensional spatial signal. The results of the diagonal details of the wavelet analysis of secondary modes shape show the turbulence of the wavelet coefficients, compared with primary modes shape in damage locations; so that, wavelet analysis of the modes shape of the first mode, show damage location with the better equivalence of wavelet coefficients and the error of less than 6%.

Conference Name: International Symposium on Inertial Sensors and Systems (ISISS) Date of Conference: 08-11 May 2022 Disk resonator gyroscopes (DRGs) utilize the circular symmetry of a set of concentric rings to realize high-performance MEMS gyroscopes. We set forth an analytical method to calculate the mode shapes of the rings and then obtain the corresponding modal mass, Coriolis mass, and stiffness. Following the Ritz method, we minimize the total potential energy of the rings subject to the boundary conditions imposed by the spokes that connect the rings. We show the efficacy of our method using the frequency response of a fabricated DRG and comparison with the finite element method (FEM). With respect to the FEM, our modeling is more straightforward, more intuitive, and can be extended to model imperfections and ensuing effects such as quadrature error and frequency split.

The Applied Element Method (AEM) is a numerical method of structural analysis. The degrees of freedom are located at the centroid of an element, which is rigid. In AEM, many pairs of springs are provided on the faces of the element. Although the AEM is very efficient, it is not popular due to the limited literature discussing stiffness matrix of AEM in detail. In this paper, the formulation of the stiffness matrix for two-dimensional and three-dimensional analysis by AEM is discussed. To improve the accuracy of AEM, a simplified stiffness matrix is developed when an infinite number of springs is considered. The strains, stresses, bending moment and shear forces are also derived. The efficiency of AEM is studied by solving a few conventional problems on beams. Comparison of AEM with FEM is also done. The AEM could predict displacements, strains, stresses, bending moment, shear force, natural frequency and mode shapes with reasonable accuracy.

As much as there has been a significant increase in the development of railway systems in recent years, one of the significant drawbacks on this mode of transport is ground-borne vibrations and noise emanating from vehicle-track interaction in service. This greatly affects the ecology and physical surroundings of the railway track. Experimental tests and Finite Element modal and complex eigenvalue analysis are conducted to investigate the dynamics of a traction wheelset and rail track. This is done to establish the correlation between the short pitch rail corrugation in the Belfast to Steelpoort railway line, in the Limpopo Province of South Africa, with railway wheel-tract resonance at low frequencies of excitation. A 3D Finite Element Method (FEM) and complex eigenvalue analysis are used to validate the resonance modes of the wheelset and rail track obtained through experimental modal analysis. Mode shapes are determined for natural frequencies that match the excitation frequency induced by short pitch rail corrugation. The results show that based on average train speeds around track curves, the excitation frequency induced by corrugation matches (quite reasonably) natural frequencies of the wheelset. Whilst the wheelset FEM results are in better agreement, they rather prove the correlation to occur at 100 Hz. In a previous study by the authors, at the average speeds per track curve, the corrugation excitation frequency was found to be 108 Hz. The current study goes further by investigating natural frequencies of rail tracks. Moreover, mode shapes of a traction wheelset and rail tracks are also investigated, and the results are presented herein.

The increasing penetration of inverter-based resources is affecting the overall power system security, so that effective tools are needed to provide system awareness and identify the most suited countermeasures. To tackle this problem, real-time monitoring and assessment of transmission grids based on synchrophasor measurements have drawn the attention of many researchers over the last decade, thanks to the high temporal resolution of data provided by phasor measurement units. In this study, a new version of the dynamic mode decomposition (DMD) is proposed as a tool for the real-time identification of electromechanical oscillations. This approach is able to provide information on the dynamic characteristics (frequency and damping) and the spatial correlation (mode shape) of the modes identified. Besides, an improved criterion is used to track and discern the dominant modes. The effectiveness of the DMD method has been tested on the two-area Kundur system and validated using data from a real event on the European synchronous grid, giving promising results. Thanks to its reliability and robustness, the DMD is now implemented in the Terna (the Italian transmission system operator) Wide Area Measurement System in use in the control room.

The ultra-low frequency oscillation (ULFO) problem reappears in China recently. Different from the classical low frequency oscillation (LFO), the generators in ULFO have the same mode shapes, namely oscillating in the same pace. To reveal the reason why ULFO generators do not oscillate inversely as classical LFO does, this paper investigates the mechanism of ULFO based on improved Philips-Heffron model of two-machine system. Through this model, the phase angle relationship between different generators is obtained. Based on the bode diagram, it is found that the phase angle difference of the two machines is around zero in ultra-low frequency band however the generator parameters change. On the contrary, the situation is different in classical low frequency band, which reveals the mechanism that generators in ULFO always oscillate in the same pace. Finally, the analysis above is validated through a 2-area 4-machine system and a 6-machine system established in PSASP software.

International audience; The femoral stem primary stability achieved by the impaction of an ancillary during its insertion is an important factor of success in cementless surgery. However, surgeons still rely on their proprioception, making the process highly subjective. The use of Experimental Modal Analysis (EMA) without sensor nor probe fixation on the implant or on the bone is a promising non destructive approach to determine the femoral stem stability. The aim of this study is to investigate whether EMA performed directly on the ancillary could be used to monitor the femoral stem insertion into the bone. To do so, a cementless femoral stem was inserted into 10 bone phantoms of human femurs and EMA was carried out on the ancillary using a dedicated impact hammer for each insertion step. Two bending modes could be identified in the frequency range [400–8000] Hz for which the resonance frequency was shown to be sensitive to the insertion step and to the bone-implant interface properties. A significant correlation was obtained between the two modal frequencies and the implant insertion depth (R2 = 0.95 ± 0.04 and R2 = 0.94 ± 0.06). This study opens new paths towards the development of noninvasive vibration based evaluation methods to monitor cementless implant insertion.

Bir yapıyı, makinayı veya mekanik sistemi meydana getiren tipik elemanlardan biri de elastik kirişlerdir. Çalışma koşulları altında kirişlerde enine titreşimler meydana gelebilir. Bunun sonucunda ortaya çıkabilecek sakıncalardan kaçınmak için endüstriyel amaçla tasarım şekillendirilirken titreşimle ilgili karakteristikler de dikkate alınmaktadır. Bu nedenle doğal frekans, mod sönüm oranı ve mod şekli olmak üzere elemanın serbest titreşim karakteristiklerinin bilinmesi gerekir. Bu çalışmada, iki ucu serbest düşey ve yatay duran alüminyum kiriş için ivmeölçer kullanılarak titreşim ölçüm uygulamaları yapılmıştır. İvmeölçer ile ölçüm yapmak için Vibroport 80 portatif titreşim ölçüm cihazı ve LabVIEW altında çalışan Ölçüm Ünitesi olmak üzere iki farklı enstrüman kullanılmıştır. Ölçüm Ünitesi, gerekli aletlerden ve aletlerin LabVIEW altında çalışmasını sağlamak üzere hazırlanmış bilgisayar programından oluşmaktadır. Çalışmanın amacı, cihaz ve Ölçüm Ünitesi’nin kiriş enine titreşimlerinin ölçümünde kullanımı bakımından araştırma yapmaktır. Portatif ve kompakt yapısı nedeniyle Vibroport 80 cihazı endüstriyel ortamlarda kullanım açısından pratiklik sağlamaktadır. Cihazda bulunan hazır program modülleri ivme frekans cevabını göstermektedir. Sonuçlar frekans bazında kaydedilebilmektedir. Teorik ve ölçüm değerlerine dayalı sonuçlar arasında, sınır şartlarının gerçekleştirilmesinden kaynaklı olabilecek farkların en az olması için her iki ucunda da serbest sınır koşulu bulunan dikdörtgen kesitli alüminyum kiriş kullanılmıştır. Serbest sınır koşullarının gerçeğe en yakın olmasını sağlamak amacıyla askı bağlantısı esnek elemanla gerçekleştirilmiştir. Darbe çekici ile kirişe vurmak suretiyle impuls kuvvet girdisi tatbik edilmiştir. Uygulanan tahrik kuvveti kirişin elastik denge halini bozmaktadır. Uygulama sırasında malzemesi farklı üç adet uç kullanılmıştır. Bundan amaç impuls girdinin tahrik süresini dolayısıyla girdi frekans değerini değiştirmektir. Bu durum daha büyük doğal frekans değerlerinin deneysel olarak elde edilmesine olanak sağlamaktır. İmpuls kuvvetin ve kiriş ivme değerlerinin zamana bağlı değişimine ait veri kümesi Ölçüm Ünitesi ile TDMS formatında dosyalara kaydedilebilmektedir. Bu işlem LabVIEW ortamında hazırlanan bilgisayar programları ile gerçekleştirilmiştir. Deneysel çalışmalar ile elde edilen doğal frekans değerlerinin, teorik hesaplar sonucu bulunan değerler ile yaklaşık olarak aynı çıktığı görülmüştür., Elastic beams are one of the typical elements that make up a structure, machine or mechanical system. Transverse vibrations can occur in beams under operating conditions. In order to avoid the inconveniences that may arise as a result of this, vibration-related characteristics are also taken into account while shaping the design for industrial purposes. For this reason, the free vibration characteristics of the element, such as natural frequency, mode damping ratio, and mode shape, must be known. In this study, vibration measurement applications have been made using accelerometers for an aluminum beam that is free vertical and horizontal at both ends. Two different instruments, the Vibroport 80 portable vibration measuring device and the Measurement Unit operating under LabVIEW, were used to measure with the accelerometer. The Measurement Unit consists of the necessary instruments and a computer program designed to enable the instruments to work under LabVIEW. The aim of the study is to investigate the use of the device and the Measurement Unit in the measurement of beam transverse vibrations. Due to its portable and compact structure, the Vibroport 80 device provides practicality in terms of use in industrial environments. Readymade program modules in the device show the acceleration frequency response. Results can be recorded on a frequency basis. A rectangular aluminum beam with free boundary conditions at both ends was used in order to minimize the differences between the theoretical and measurement results based on the realization of boundary conditions. In order to ensure that the free boundary conditions are closest to reality, the suspension connection is made with a flexible element. Impulse force input is applied by hitting the beam with impact hammer. The applied driving force disrupts the elastic equilibrium state of the beam. During the application, three tips of different materials were used. The purpose of this is to change the excitation time of the impulse input, hence the input frequency value. This is to allow larger natural frequency values to be obtained experimentally. The data set of the time dependent variation of the impulse force and beam acceleration values can be saved to files in TDMS format with the Measurement Unit. This process was carried out with computer programs prepared in the LabVIEW environment. It has been observed that the natural frequency values obtained by experimental studies are approximately the same as the values found as a result of theoretical calculations.

The transmission of engine vibration to the supporting structure can be prevented by using flexible mounting, such as steel springs or elastomeric material. A flexibly mounted rigid body has natural frequencies of vibration in the 6 degrees of freedom. The challenge is resonance situations, where the natural frequencies match with engine excitation frequencies, causing vibration amplification. To prevent resonance, flexible mounting must be designed so that the natural frequencies are far enough from the excitation frequencies. According to the lumped mass theory, internal bending, and torsional moments due to balanced forces of engine, don’t excite the rigid body modes. For this reason, the internal excitations have not been considered in design of flexible mounting systems. However, vibration levels have been noticed to increase in resonance situations, even if the forces in the engine had been well balanced. The aim of this thesis was to find out if the internal bending and torsional moments excite the rigid body modes in practice. The research question was answered by performing vibration measurements for flexibly mounted engines and analysing the results. The literature review focuses on engine excitation mechanics and basics of rigid body dynamics. Calculation software were utilized for calculating engine excitations and rigid body natural frequencies and mode shapes. The work showed that the internal moments excite the engine rigid body modes. The result was achieved changing engine natural frequencies in relation to excitation frequencies and studying motion behaviour of the engine with different configurations. Tuning of the natural frequencies was possible by turning rubber elements that had different stiffness for longitudinal and horizontal directions. Operating deflection shape corresponded to rigid body motion when the natural frequency was tuned near the excitation frequency. When natural frequency was tuned out of internal excitation frequency, the operating deflection shape corresponded to the bending or twisting due to internal moment. Amplitude of vibration was also higher in the resonance situation. Change in engine load was seen as change of amplitude at a rigid body natural frequency. That also gives evidence internal torsional excitation caused by gas forces excites rigid body mode. The results were confirmed repeating measurements for three engine types. It is obvious internal excitations must be considered in response calculations and in design of flexible mounting systems. Response calculations of flexibly mounted engines have been done with simple program based on lumped mass model assuming the mounted structure to be rigid. Internal excitations aren’t thus taken into account by the program. On the other hand, calculating responses with FEM-based program is too laborious and time consuming. It could be studied what kind of force must be entered into the program for simulating rigid body response caused by internal moment. In this way the use of the fast and designer-oriented program could be continued in the future. Moottorin värähtelyn siirtymistä tukirakenteeseen voidaan estää käyttämällä kiinnitykseen joustavia elementtejä kuten teräsjousia tai elastomeerimateriaalia. Joustavasti asennetulla jäykällä kappaleella on kuusi ominaistaajuutta ja -muotoa, joilla sen on ominaista värähdellä. Haasteeksi muodostuvat resonanssitilanteet, joissa ominaismuodolla on sama taajuus kuin moottorin herätevoimalla, jolloin värähtely voimistuu. Resonanssin välttämiseksi, joustava asennus tulee mitoittaa siten, että ominaistaajuudet ovat tarpeeksi kaukana herätetaajuuksista. Jäykän kappaleen teorian mukaan moottorin tasapainotetuista voimista aiheutuvat sisäiset taivutus- ja vääntömomentit eivät herätä jäykän kappaleen ominaismuotoja. Tämän vuoksi mitoituksessa ei ole huomioitu sisäisiä herätteitä. Käytännössä on kuitenkin havaittu tärinätasojen nousevan resonanssitilanteessa, vaikka moottori olisi hyvin tasapainotettu. Työn tarkoituksena oli selvittää, herättävätkö sisäiset taivutus- ja vääntömomentit jäykän kappaleen ominaismuodot käytännössä. Tutkimuskysymykseen saatiin vastauksia suorittamalla värähtelymittauksia joustavasti asennetuille moottoreille ja analysoimalla mittaustuloksia. Työssä syvennyttiin kirjallisuuden avulla moottoreiden herätemekaniikkaan ja jäykän kappaleen dynamiikan perusteisiin. Laskentaohjelmistoja hyödynnettiin moottoriherätteiden sekä jäykän kappaleen ominaistaajuuksien- ja muotojen laskemiseen. Työssä osoitettiin, että sisäiset momentit herättävät moottorin jäykän kappaleen ominaismuodot. Tulokseen päästiin muuttamalla moottorin ominaistaajuuksia herätetaajuuksiin nähden ja tutkimalla moottorin liikekäyttäytymistä eri konfiguraatioilla. Ominaistaajuuksien viritys onnistui kääntämällä kumielementtejä, joilla on eri jäykkyys pituus- ja leveyssuuntiin. Käynninaikainen värähtelymuoto vastasi jäykän kappaleen ominaismuotoa, kun ominaistaajuus oli viritetty lähelle sisäisen herätteen taajuutta. Kun ominaistaajuus viritettiin pois sisäisen herätteen alueelta, käynninaikainen värähtelymuoto vastasi sisäisen momentin aiheuttamaa taipumaa tai vääntöä. Myös värähtelyn amplitudi oli selkeästi korkeampi resonanssitilanteessa. Moottorin kuormituksen muutos nähtiin amplitudin muutoksena jäykän kappaleen ominaistaajuudella. Tämä antaa myös näyttöä siitä, että kaasuvoimista aiheutuva sisäinen vääntöheräte herättää jäykän kappaleen liikkeen. Tulokset vahvistettiin toistamalla mittauksia kolmelle moottorityypille. On selvää, että sisäiset herätteet tulee huomioida joustavien asennusten suunnittelussa ja vastelaskennassa. Joustavasti asennetun moottorin vastelaskentaa on tehty yksinkertaisella jousi-massateoriaan perustuvalla ohjelmalla, joka olettaa kiinnitetyn rakenteen jäykäksi, eikä se siten huomioi sisäisiä herätteitä. Vasteiden laskenta FEM-ohjelmalla taas ei tule kysymykseen sen vaatiman ajan ja työpanoksen suhteen. Jatkossa voitaisiin tutkia, millainen voima ohjelmaan pitää syöttää, jotta saataisiin simuloitua sisäisen momentin aikaansaama jäykän kappaleen vaste. Tällöin nopeaa, suunnittelijalähtöistä ohjelmaa voitaisiin käyttää myös tulevaisuudessa.

Vibration sensors are mostly used for fault diagnoses of machines or structures. If more sensors are applied, more accurate fault diagnosis is possible. However, it will obviously cost more. There are many approaches to optimize the number and installation location/point of vibration sensors for more efficient fault diagnosis. Existing methods require a great deal of computational throughput for optimization when considering many mode frequencies with points where vibration sensors are likely to be installed. This paper proposes a practical way of optimizing the sensor installation point considering many mode frequencies with lots of places for sensor installation. FEA was conducted to identify displacement values of each frequency in the candidate points. Then, correlation coefficients were applied to the FEA result to optimize the installation location and number of vibration sensors. Taking into account cases where the number of sensors has been set by users, FIM was applied. The correlation coefficient optimized the candidate points where 24,252 vibration sensors were to be installed and reduced this to 10 points. FIM, which was not suitable for directly optimizing sensor locations because it required a lot of computational throughput and was usually applied to evaluate other methods, is now applicable to candidate points that have been reduced by the correlation coefficient. This paper does not draw the best optimal sensor location but presents a way to apply to large-scale or complicated forms with a little computational throughput.

A mode shape is a specific pattern of vibration executed by a mechanical system at a specific frequency. Different mode shapes will be associated with different frequencies. The experimental technique of modal analysis discovers these mode shapes and the frequencies. In this paper modal analysis has been carried out to determine the mode shapes and the respective frequencies of perforated plates with regard to change in the dimension of the perforations and the distance between the perforations (pitch).

Estimation and monitoring of cable tension is of great significance in the structural assessment of cable-supported bridges. For short cables, the traditional cable tension identification method via frequency measurement has large errors due to the influence of complex boundaries, which affect the accuracy of estimation. A new cable tension estimation method based on mode shape identification with a multiple sensor arrangement on the cable can take the influence of boundary conditions into account and its accuracy has been verified. However, it requires more sensors compared to the traditional frequency-based method, which will significantly increase the cost of long-term monitoring in practice. Therefore, a novel approach for cable tension monitoring considering both cost and accuracy is further proposed in this study. The approach adopts multiple sensors to measure the influence of boundary conditions. Then, only a single sensor is required for long-term monitoring of the cable. In this paper, an analytical model of the cable is firstly established. The influence of boundary conditions is calculated, which ensures the accuracy of mode shape identification. Furthermore, a field experiment is carried out to verify the effectiveness of the new approach. The results have demonstrated the effectiveness and accurateness of the proposed method in long-term short cable tension monitoring.

Light absorption induced thermoelastic and photoacoustic excitation, combined with laser Doppler vibrometry, was utilized to analyze the dynamic mechanical behavior of a microcantilever. The measured frequency response, modal shapes, and acoustic coupling effects were interpreted in the framework of a simple Bernouilli-Euler model and quantitative 3D finite element method (FEM) analysis. Three opto-mechanical generation mechanisms, each initiated by modulated optical absorption and heating, were identified both by an analytical and finite element model. In decreasing order of importance, optically induced cantilever bending is found to be caused by: (i) differences in photoacoustically induced pressure oscillations in the air adjacent to the illuminated and dark side of the cantilever, resulting from heat transfer from the illuminated cantilever to the nearby air, acting as a volume velocity piston, and (ii) thermoelastic stresses accompanying temperature and thermal expansion gradients in the cantilever, (iii) photoacoustically induced pressure oscillations in the air adjacent to the illuminated cantilever holder and frame. ispartof: PHOTOACOUSTICS vol:24 ispartof: location:Germany status: published

In most experimental investigations, the accelerometer mass effect is neglected since the accelerometer mass is small in comparison to the mass of the test construction. When a lightweight construction is examined, however, this impact is noticeable. The goal of this research is to see how mass affects thin plate vibration. The characteristics of interest were the natural frequency and its associated mode shape. Using finite element analysis, the thin plate simply supported boundary condition was studied. The mass was added to the plate and distinct sites were chosen for mounting. The mass has a considerable influence on certain of the structure's modes, while it has no effect on others, according to the findings. The mass, which was placed at the plate's highest deflection point, revealed significant variations in natural frequencies and their associated mode shapes. For the mass mounted at the nodal line of the specific mode, there are no notable changes in natural frequency or mode shapes. The influence of mass is found to be dependent on the position of the mass, the vibration mode, and the magnitude of the mass. &nbsp

The main principle of vibration-based damage detection in structures is to interpret the changes in dynamic properties of the structure as indicators of damage. In this study, the mode shape damage index (MSDI) method was used to identify discrete damages in plate-like structures. This damage index is based on the difference between modified modal displacements in the undamaged and damaged state of the structure. In order to assess the advantages and limitations of the proposed algorithm, we performed experimental modal analysis on a reinforced concrete (RC) plate under 10 different damage cases. The MSDI values were calculated through considering single and/or multiple damage locations, different levels of damage, and boundary conditions. The experimental results confirmed that the MSDI method can be used to detect the existence of damage, identify single and/or multiple damage locations, and estimate damage severity in the case of single discrete damage.

In this paper, the vibration analysis in terms of modal and harmonic responses are investigated for the power station structure of Kenyir Dam in Terengganu, Malaysia. Modal analysis is carried out to provide the dynamic characteristics of the power station which includes the natural frequencies and mode shapes. Meanwhile, the harmonic response analysis is performed by applying the force to the structure to obtain the Frequency Response Function (FRF) in certain range of frequencies. A real scale three-dimensional (3D) model of the Kenyir Dam power station is constructed using SolidWorks software and imported to ANSYS software for the Finite Element (FE) analysis. A proper boundary condition is taken into consideration to demonstrate the real behaviour of the power station structure. From the results, six most significant natural frequencies and mode shapes including the FRF in all three axes are selected. The highest natural frequency value occurred at 5.4 Hz with the maximum deflection of 0.90361 m in the z axis direction. This value is important in order to verify whether the structure can overcome the resonance phenomenon from the external disturbance forces in the future.

The vibration of the barrel, induced by the interaction with a high-speed moving projectile, has a considerable influence on the shooting accuracy of a weapon. The finite element model of a multi-barrel was established with the goal to investigate its vibration characteristics in this paper, and the natural frequency and mode shape were analyzed by finite element method. To verify the result of finite element modal analysis (FEMA), a modal testing system basis on SC310W multi-path data-collecting system and hammer hitting method was set up. Results show that the low order vibrations of the multi-barrel artillery were mainly vertical, horizontal and torsional vibration, but the local vibration at high orders. The error of natural frequencies between the results obtained by simulation and test was 8.82 % in the first mode frequency and 1.37 % in the eighth. The FEMA can effectively simulate the actual vibration of the multi-barrel artillery.

Made available in DSpace on 2019-10-06T17:14:04Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-09-01 There are well-known expressions for natural frequencies and mode shapes of a Euler-Bernoulli beam which has classical boundary conditions, such as free, fixed, and pinned. There are also expressions for particular boundary conditions, such as attached springs and masses. Surprisingly, however, there is not a method to calculate the natural frequencies and mode shapes for a Euler–Bernoulli beam which has any combination of linear boundary conditions. This paper describes a new method to achieve this, by writing the boundary conditions in terms of dynamic stiffness of attached elements. The method is valid for any boundaries provided they are linear, including dissipative boundaries. Ways to overcome numerical issues that can occur when computing higher natural frequencies and mode shapes are also discussed. Some examples are given to illustrate the applicability of the proposed method. São Paulo State University (UNESP) School of Engineering Zayed University Dalian University of Technology Institute of Internal Combustion Engine São Paulo State University (UNESP) School of Engineering

This paper proposes an approach to extract the mode shapes of beam-like structures from the dynamic response of a moving mass. When a mass passes through a beam containing several artificially installed humps, its vertical acceleration can be recorded. After applying fast Fourier transformation to the dynamic response, one can extract the mode shapes of the beam. The surface roughness was neglected compared to the humps and its adverse effect on the extraction was reduced. The passing mass performs as both “exciter” and “massage receiver”; therefore, this method requires only one single accelerometer, making it more convenient and time saving in practice. Moreover, to estimate the possible error in extracting mode shapes, a wavenumber domain filtering technique is used to reconstruct the general profiles of mode shapes. Experimental validation of this approach in laboratory scale was conducted. The experimental results show that the proposed method performs well in extracting lower order mode shapes. It should also be noted that the passing mass can not have a very high velocity (e.g. 80 mm/s), otherwise the mass may jump and separate from the beam, and the proposed method may fail to identify mode shapes.

Corner-supported modular structures are made of repetitive prefurnished, prefinished modular units, which are fabricated in a factory and transported to the site of a building to form a permanent building block. The modular units are then tied together through the use of so-called inter-modular connections, or inter-connections, which form a different configuration at joints compared to conventional steel structures. The presence of inter-connections in these structures, in addition to beam-to-column connections or intra-connections, may change their dynamic characteristics, including natural frequencies, mode shapes, and damping ratios. This paper aims to investigate the dynamic characteristics of a modular building through the use of operational modal analysis (OMA). A half-scaled three-storey modular structure, designed and instrumented with highly sensitive accelerometers, was experimentally tested under pure and randomly generated vibrations. The time history of the response acceleration of the structure was recorded using a data acquisition system. Different output-only techniques of OMA, based on both frequency and time domains, were employed to analyse the recorded response acceleration of the structure and extract the natural frequencies, mode shapes, and damping ratios. These techniques are peak picking (PP), enhanced frequency-domain decomposition (EFDD), and stochastic subspace identification (SSI). The outcomes in this paper can be used for further research on the development of an experimental formula for the design of multistorey modular buildings against lateral loads.

The loading and response of structures due to gust buffeting is a dominant topic of wind engineering. One of its crucial aspects is the shape of vibration modes. Although numeric solutions ...

Dagens planering och projektering av konstruktioner präglas av ett resursutnyttjande, miljömässigt och ekonomiskt tänk, där resultatet kan medföra brister med avseende på dynamiken. Därmed är det ytterst viktigt att skapa goda förutsättningar för noggranna beräkningsmodeller som i ett projekteringsskede kan representera konstruktionernas dynamiska beteende. I denna rapport utfördes en jämförelseanalys mellan en FE-modell och en fältmätning, där Folke Bernadottes bro har använts som underlag. Syftet är att presentera skillnader och likheter i naturliga frekvenser och modformer baserat på jämförelseanalysen, samt belysa några av de viktigaste faktorerna bakom dessa. Resultatet visade för en kalibrerad FE-modell 11 % genomsnittlig skillnad för de naturliga frekvenserna och 99 % överensstämmelse med avseende på modformerna, där den mest väsentliga parametern i modellen var upplagsvillkoren. Today's planning and design of constructions is characterized by a resource utilization, environmental and economic thinking, where the result can lead to shortcomings with regard to dynamic behaviour. Thus, it is extremely important to create good conditions for accurate calculation models that in a design phase can represent the dynamic behaviour of the structures. In this report, a comparison analysis was performed between an FE-model and a field measurement, where Folke Bernadotte's bridge has been used as basis. The purpose is to present differences and similarities in natural frequencies and mode shapes based on the comparative analysis, and to highlight some of the most important factors behind these. The result showed for a calibrated FE-model an average difference of 11 % for the natural frequencies and 99 % agreement with respect to the mode shapes, where the most important parameter in the model was the support conditions.

In the present work, for the first time, free vibration response of angle ply laminates with uncertainties is attempted using Multivariate Adaptive Regression Spline (MARS), Artificial Neural Network-Particle Swarm Optimization (ANN-PSO), Gaussian Process Regression (GPR), and Adaptive Network Fuzzy Inference System (ANFIS). The present approach employed 2D C0 stochastic finite element (FE) model based on the Third Order Shear Deformation Theory (TSDT) in conjunction with MARS, ANN-PSO, GPR, and ANFIS. The TSDT model used eliminates the requirement of shear correction factor owing to the consideration of the actual parabolic distribution of transverse shear stress. Zero transverse shear stress at the top and bottom of the plate is enforced to compute higher-order unknowns. C0 FE model makes it commercially viable. Stochastic FE analysis done with Monte Carlo Simulation (MCS) FORTRAN inhouse code, selection of design points using a random variable framework, and soft computing with MARS, ANN-PSO, GPR, and ANFIS is implemented using MATLAB in-house code. Following the random variable frame, design points were selected from the input data generated through Monte Carlo Simulation. A total of four-mode shapes are analyzed in the present study. The comparison study was done to compare present work with results in the literature and they were found in good agreement. The stochastic parameters are Young&rsquo, s elastic modulus, shear modulus, and the Poisson ratio. Lognormal distribution of properties is assumed in the present work. The current soft computation models shrink the number of trials and were found computationally efficient as the MCS-based FE modelling. The paper presents a comparison of MARS, ANN-PSO, GPR, and ANFIS algorithm performance with the stochastic FE model based on TSDT.

IN THIS WORK, CARBON FIBRE REINFORCED POLYMER (CFRP) PLATES HAVE BEEN TESTED UNDER FREE IMPACT VIBRATION TESTS IN PRISTINE AND DAMAGED CONFIGURATIONS. EACH DAMAGED PLATE INVOLVED ONE CRACK OF SPECIFIC ORIENTATION (HORIZONTAL, VERTICAL, AND DIAGONAL). THE PLATES WERE SUSPENDED AS CANTILEVERS AND VIBRATED USING AN IMPACT HAMMER. TWO ACCELEROMETERS AND ONE MICROPHONE WERE USED TO OBTAIN THE VIBRATION RESPONSE DATA SIGNALS FROM THE PRISTINE AND DAMAGED PLATES, AND THE FREQUENCY RESPONSE FUNCTION (FRF) WAS PLOTTED. THE CFRP PLATES WERE ALSO SUBJECTED TO A TENSILE TEST AND TO SCANNING ELECTRON MICROSCOPY (SEM), THEREBY ESTIMATING THEIR MECHANICAL PROPERTIES AND EVALUATING THEIR CARBON FIBRE MICROSTRUCTURES. THE CURRENT TECHNIQUE FOCUSED ON THE DETECTED SIGNAL FROM MORE THAN ONE VIBRATION SENSOR TO ENSURE THE MEASUREMENT'S ACCURACY. COMPARISONS BETWEEN THE EXPERIMENTAL VIBRATION TEST AND THE FINITE ELEMENT ANALYSIS (FEA) SIMULATION SHOWED THAT THE RESULTS AGREED. THE DAMAGE ORIENTATION SIGNIFICANTLY AFFECTED THE COMPOSITES’ DYNAMICPROPERTIES. THE FRF MEASURES OF THE DAMAGED CFRP COMPOSITES SHOWED THE LOWEST EIGENVALUES FOR THE EXCITED MODE SHAPES' RESONANT FREQUENCIES. THE 0/90 LAYUP LAMINATE COMPOSITE EXHIBITED GREATER FLUCTUATIONS IN RESONANT FREQUENCIES ACROSS THE VARIOUS MODE SHAPES THAN DID THE QUASI-ISOTROPIC LAMINATES. THE RESONANT FREQUENCY FLUCTUATIONS IN THE 0/90 LAYUP LAMINATE REACHED A 2.85% DIFFERENCE COMPARED TO THE QUASI-ISOTROPIC LAMINATE COMPOSITES.

Studies carried out on gust buffeting and aerodynamic admittance show that mode shape represents a sort of watershed. If the mode does not change sign along the structure axis, the problem ...

This study presents the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods. To determine the natural frequency and mode shape of the double tapered cracked beam, the stiffness and mass matrices of the beam have been obtained. The crack in the beam is modeled as a massless spring, and the beam is divided into two subcomponents from the crack section. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expressions. It has been observed that natural frequencies and mode shapes vary depending on the location of the crack, the depth of the crack and the aspect ratios of the beam. The results of the present study and those in the literature are compared and a great deal of consistency has been found.

International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies, 12, 9, 12A9A: 1-8

This paper aims at presenting the guidelines to follow in order to set up an identification procedure which is able to determine the axial force, the flexural rigidity and the rotational end stiffnesses of slender and tensioned structural elements, based on measurements of their natural frequencies and mode shapes. First of all, when such an element is slightly affected by bending stiffness effects, perturbation methods can be applied to get a composite approximation for its natural frequencies and an asymptotic expression for its mode shapes. These simple analytical formulas allow to understand the role played by each model parameter in the modal response and show that the axial force, the flexural rigidity and the rotational end stiffnesses can be correctly identified under some conditions, which are established and provided in this document. Among others, it is necessary that the identification procedure relies on the first few natural frequencies and mode shapes, which are measured near each extremity of the element, as well as some natural frequencies associated with higher modes.

Timber is a building material that is becoming more common and of interest for use in high-rise buildings. One of the reasons is that timber requires less energy input for the manufacturing process of the material compared to non-wood based materials. When designing high- rise timber buildings it is of great significance to understand the dynamic behavior of the structure. One method to obtain the dynamic properties is to use Operational Modal Analysis, which is based on the structural response from operational use. Finite element (FE) analysis is a tool which can be used for dynamic analysis for large structures. In this study an Operation Modal Analysis (OMA) was conducted on a four-story timber building in Växjö. A finite element model was created of the same building using commercial FE packages. Based on the mode shapes and natural frequencies obtained from the OMA, the FE model was fine-tuned. The purpose of this thesis is to gain knowledge of which parameters that might have a significant role in finite element modelling for a structural dynamic analysis. The aim is to develop a finite element model that accurately simulates the dynamic behavior of the tested building. It was shown from the result that is possible with an enough detailed FE model to capture the dynamic behaviour of a structure. The parameters that had the largest effect on the result can be pointed to the mass and the stiffness of the structure. Trä är ett byggnadsmaterial som börjar bli allt mer vanligt och är av intresse att använda som stommaterial för höga byggnader. En anledning till detta är att det krävs mindre energi i tillverkningsfasen för trä jämfört med stål och betong. Vid dimensionering av höga träbyggnader är det essentiellt att förstå byggnadens dynamiska egenskaper. För att ta fram en byggnads dynamiska egenskaper kan en metod som benämns Operational Modal Analysis (OMA) tillämpas vilken baseras på byggnadens rörelser vid daglig användning. Finita element (FE) metoden är ett verktyg som kan användas vid dynamisk analys för större byggnader. I detta arbete genomfördes en OMA för ett fyravåningshus med trästomme beläget i Växjö. Genom användning av kommersiella FE-mjukvaror togs en finita element modell av samma byggnad fram. Baserat på de egenfrekvenser och egenmoder erhållna från OMA, uppdaterades FE-modellen därefter. Syftet med detta arbete är att erhålla kunskap kring vilka parametrar som har betydelse vid FE-modellering med hänsyn till dynamisk analys. Syftet är även att validera den prototyp av datainsamlingsenhet som använts vid fältmätningen. Målet med arbetet är att ta fram en FE-modell som på ett korrekt sätt beskriver den testade byggnadens dynamiska beteende. Resultatet av arbetet påvisar att med en tillräckligt detaljerad FE-modell är det möjligt att erhålla en byggnads dynamiska egenskaper. De parametrar som har störst inverkan på resultatet är byggnadens styvhet och inkluderad massa.

Texte intégral accessible uniquement aux membres de l'Université de Lorraine jusqu'au 1er janvier 2022.; This study presents an experimental and numerical investigation on the vibrational serviceability performance of novel adhesive free engineered wood products (AFEWPs), namely adhesive free laminated timber beams (AFLB) and adhesive free cross-laminated timber panels (AFCLT), assembled through thermo-mechanically compressed wood dowels (CWD). The experimental modal analyses were carried out under free-free conditions using a hammer impact. Natural frequencies, mode shapes, and damping ratio were assessed experimentally. In addition, similar glued timber beams (conventional glulam) were manufactured and tested for comparison purpose. A 3D FE model was developed and validated by comparison against experimental data and then used to predict the vibrational behavior of a realistic flooring system made with AFCLT panel measuring 4.5 m x 5.5 m. A parametric study was performed on the FE model to maximize the floor stiffness. The predicted FE results were discussed with regard to the Eurocode 5 vibrational serviceability design requirements showing acceptable vibrational performance. A simplified FE model was then developed to reduce computational cost. The variability level of the results for the AFEWPs was also studied and discussed. The numerical variability of frequencies of the AFEWPs was investigated based on the development of the Modal Stability Procedure (MSP). The MSP result was first compared with the FE result in the nominal case. Then, the statistic results (mean value, standard deviation, coefficient of variation and distribution) obtained from the MSP were compared with the results from the classical method (direct Monte Carlo simulation) and experimental results. A quick error estimation between the MSP and the direct Monte Carlo simulation was developed. Finally, the mean and standard deviation of the frequencies of the realistic AFCLT flooring system were predicted by the MSP.; Cette thèse présente une étude expérimentale et numérique sur les aptitudes en service en ce qui concerne le comportement vibratoire de planchers réalisés en bois d’ingénierie sans colle (AFEWP), à savoir les poutres en bois lamellé sans adhésif (AFLB) et les panneaux en bois lamellé-croisé sans adhésif (AFCLT), assemblés par des tourillons en bois densifié (CWD). Les analyses modales expérimentales ont été réalisées en conditions libres-libre à l'aide d'un marteau instrumenté. Les fréquences naturelles, les modes propres et les coefficients d'amortissement ont été évalués expérimentalement. De plus, des poutres en bois lamellé-collé similaires ont été fabriquées et testées à des fins de comparaison. Un modèle EF 3D a été développé et validé par comparaison avec des données expérimentales, puis utilisé pour prédire le comportement vibratoire d'un système de plancher à grande échelle réalisé avec un panneau AFCLT mesurant 4,5 m x 5,5 m. Une étude paramétrique a été réalisée en utilisant le modèle EF pour identifier les paramètres qui influent sur la rigidité et les fréquences propres du plancher. Les résultats obtenus ont été analysés au regard des critères de conception exigés par Eurocode 5 en ce qui concerne le confort vibratoire des planchers bois. Un modèle EF simplifié a ensuite été développé pour réduire les coûts de calcul. Le niveau de variabilité des résultats des AFEWP a été également étudié et discuté. La variabilité numérique des fréquences des AFEWP a été étudiée en utilisant la méthode MSP (Modal Stability Procedure). Les résultats de la méthode MSP ont d'abord été comparés aux résultats EF dans le cas nominal. Les résultats statistiques (valeur moyenne, écart type, coefficient de variation et distribution) obtenus par la méthode MSP ont été confrontés aux résultats de simulation directe de Monte Carlo ainsi qu’aux données expérimentales. Une estimation rapide des erreurs entre la méthode MSP et la simulation directe de Monte Carlo a été développée. Enfin, la variabilité (moyenne et écart-type des fréquences) du comportement vibratoire du système de plancher à grande échelle a été étudiée en utilisant la méthode MSP.

Structural damage identification has become an important topic in the field of civil engineering in recent years. The shear-type structure, such as shear frame structure, is a common type used in civil engineering. In this paper, a damage identification method based on the change of generalized shear energy is proposed for shear-type structures. The main steps of the proposed method are as follows. Firstly, the element stiffness matrix in the structural finite element model is decomposed to obtain the elementary shear force vector. Secondly, the elementary generalized shear energy is calculated by the dot product of the vibration mode shape vector and the elementary shear force vector. Thirdly, structural damage locations can be determined by the changes of elementary generalized shear energy. Finally, more accurate damage localization and quantification are achieved by solving the mode shape sensitivity equation. A 20-storey numerical example and a three-storey experimental model are used to demonstrate the proposed damage identification algorithm. From the numerical and experimental results, it was found that the proposed approach can accurately identify the location and extent of the damage in the shear structures even if the data contain noise. It has been shown that the presented algorithm may be useful in the damage identification of shear-type structures.

Historically, the most common cause of bridge failure has been ���scour��� ��� the gradual erosion of soil around bridge foundations due to rapid water flow. A reliable technique to monitor scour could potentially guide timely repair and, in turn, mitigate the risk of future scour-induced bridge failure. Currently, there are various, mostly underwater, techniques employed by bridge managers to monitor scour, ranging from diving inspections to autonomous underwater vehicles; however, none have gained wide acceptance. A particular disadvantage of underwater monitoring techniques is that the equipment underwater is relatively difficult to install and prone to damage from fast-flowing water and debris. One possible solution might be to use a vibration-based method to monitor scour indirectly, using changes in dynamic modal parameters (e.g. the natural frequency of vibration) captured by sensors mounted on the bridge deck or piers above the water level. There has been extensive research into the use of vibration-based monitoring methods to identify other causes of failure, such as cracking and deterioration in bridge superstructures; however, this has proven to be ineffective in practice, as the expected sensitivities in modal parameters were only single-digit percentages and therefore insufficient to overcome environmental/operational sensitivity. In contrast to superstructure damage, scour is a special damage case, which changes a boundary condition of the bridge in the form of an increase in effective pier height as a result of the lowering of the ground level and therefore, significant changes in modal parameters can be expected. Recently, this concept has been studied primarily using numerical modelling simulations of a hypothetical integral bridge with piled foundations. Only one modal parameter ��� natural frequency ��� was investigated in most of these studies and it was predicted to change by up to double-digit percentages due to scour. Although such a high change could potentially overcome environmental and operational sensitivities, a critical problem is that this has been difficult to observe in practice with experiments on either real field bridges or small-scale soil-structure models. Another problem is that there is little knowledge of the applicability of this technique to different types of bridges and forms of scour. This research proposes a vibration-based technique based on a combination of three vibration parameters (spectral density, mode shape and natural frequency), which were studied using first-of-a-kind experiments and numerical modelling simulations on various types of bridges and forms of scour. A field trial was carried out on a bridge with pre-existing scour, which was monitored for ambient vibrations throughout a repair process involving controlled scour backfilling, i.e., ���scour in reverse���. The effect of this scour backfilling was captured by measuring changes in two of these parameters, mode shape and spectral density, derived from the ambient vibrations. The mode shapes, in particular, showed the potential to localise the presence of scour to a specific pier. The most commonly measured vibration parameter of natural frequency was also observed from ambient vibrations, but this did not capture the effects of backfilling due to high measurement uncertainties. In order to study all three of these vibration parameters in a controlled environment, a centrifuge model testing programme was developed. These tests considered small-scale models representing three full-scale bridges with different bridge deck and foundation configurations (i.e. integral/ simply supported decks and shallow/deep foundations) and two forms of scour (i.e. local/global). The observed results of these small-scale centrifuge models were used to calibrate numerical models of full-scale bridges representative of these centrifuge models. Numerical simulation techniques were also developed to simulate the experimentally observed effects of local and global scour. These centrifuge experiments and the associated numerical modelling found that vibration-based methods have broad applicability for bridges, although only some parameters showed sufficient sensitivity to be viable as a monitoring technique in certain types of bridges. For example, the centrifuge bridge models with a shallow foundation did not show a significant change in natural frequency or mode shapes, but they did show a significant change in modal spectral density. This research therefore concludes that a vibration-based scour monitoring technique, examining the combined effect of natural frequency, mode shape and spectral density parameters, has significant potential to measure and even localise the change of scour depths at bridge foundations., Gates-Cambridge Scholarship (Bill and Melinda Gates Foundation grant reference number OPP1144) Laing O���Rourke Centre for Construction Engineering and Technology Cambridge Centre for Smart Infrastructure and Construction (Innovate UK Grant reference number 920035 and EPSRC Grant no EP/N021614/1)

A non-contact vision sensor system for monitoring structural displacements with advanced Zernike subpixel edge detection technique is suggested in this paper. Edge detection can detect features of objects effectively without using templates. Subpixel techniques provide more accurate and cost-effective results when compared to integer pixel methods. Built on these two techniques, a new version sensor method was developed to detect the vibrations of structures in this study. Satisfactory agreements were found between the displacements measured by the vision sensor system and those recorded by the Multipurpose Testing System (MTS). A field test was then carried out on a street sign using the proposed vision system. Satisfactory results were obtained using the new version of the sensor system at many points simultaneously without any manually marked targets. Moreover, the system was able to provide natural frequencies and mode shapes of the target instantaneously, which could be used to accurately locate damage.

This paper experimentally investigates a vibration-based scour monitoring approach applicable to bridges with multiple simply supported spans on shallow foundations. A monitoring strategy based on the relative changes in pier-mode shape amplitudes due to scour is postulated. The first global mode shape of a bridge structure with multiple spans is extracted from acceleration measurements using an output-only approach, frequency domain decomposition (FDD). The relative changes of the pier-mode shape amplitudes under scour are then tracked. Here, each pier-mode shape value is compared with the mean values of the remaining piers in a process that creates a mean-normalized mode shape (MNMS). The approach is demonstrated on a scaled model of a bridge with four spans, supported on sprung foundations, where scour is simulated by the replacement of springs, with springs of lower stiffness corresponding to a reduction in foundation stiffness. It is shown that at a given “scoured” pier, significant increases in the MNMS value occur, suggesting that the location of the scour can be identified. The magnitude of the MNMS at a given pier also increases with an increase in stiffness loss due to scour. In practice, the approach would work best by carrying out a visual inspection of the bridge to establish the initial health condition at the time of sensor installation. After this initial process, the bridge can be monitored remotely for scour on an ongoing basis. Science Foundation Ireland

This paper studies the in-plane free vibration of axially functionally graded (AFG) circular arches with non-uniform cross-section. The geometric and material properties of circular arches with regular polygon cross-section vary symmetrically about the mid-arc along the axial direction in quadratic polynomial form. The governing differential equations of the motion are derived, and the symmetric and anti-symmetric boundary conditions of the arches are developed for applying initial and boundary value problems in the solution method. The computed results agree well with the results of the finite element software ADINA. The effects of geometrical and material parameters on the natural frequency and mode shape of AFG circular arches are investigated.

The aim of the research has been to investigate the change of dynamic behavior of a Kaplan turbine runner when submerged in still water. More specifically, the effects of the added mass on the modes of vibration have been quantified. For that, the modes of vibration of the runner in vacuum, in air and in water have been simulated with a coupled Acoustic-Structural modal analysis and, from their comparison, the reduction of the natural frequencies and the possible changes of the mode shapes have been determined. The results show that the typically assumed invariance of all the mode shapes of a structure when submerged in a dense fluid is not fully accomplished in this particular geometry. And regards to the frequency reduction ratios, they are found to be similar for the first six modes with an average value of about 37%. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 814958. The authors also wish to acknowledge Vattenfall for the support.

Unlike metal structure, composite structures don’t give any clue till the fatal final collapse. The problem is more complicated when applied load on the structure is aeroelastic in nature. Under such loading, composite laminate experiences stresses. The first layer failure happens when stresses in the weakest ply exceed the allowable strength of the laminate. This initial layer-based failure changes overall material characteristics. It is important now to degrade the composite laminate characteristics for the subsequent failure prediction. The constitutive relations are required to be updated by the reduction in stiffness. The rest of the undamaged laminates continue to take the load till the updated strength is reached. In the present work, layer wise progressive failure analysis under aeroelastic loading has been performed by the inclusion of different failure criteria which allow for the identification of the location of the failure. ANSYS APDL environment has been used to model geometry of helicopter rotor. Under the loading conditions, stresses are calculated in the blade. Using stress tensor and failure criteria, failure location and modes have been predicted. It has been found that failure starts at higher speeds and failure starts from the root chord and tend towards the tip chord.

For intermediate floors in residential and office buildings, as well as in parking garages and malls, there is a wide use of hollow core concrete slabs in Sweden today. Hollow core slabs are precast and prestressed concrete elements with cylindrical-shaped voids extending along the length of the slab. These structural elements have the advantage compared to cast-in-situ concrete slabs that they have a high strength, due to the prestressing, and that the voids allow for a lower self-weight. Additionally, the voids allow for a reduction in the use of concrete material. These characteristics offer possibilities to build long-span floors with slender designs. However, a consequence of the slenderness of the slabs is that such floors have an increased sensitivity to vibrations induced by various dynamic loads. In residential and office buildings vibrations are primarily caused by human activity, and therefore concerns related to the serviceability of such floors are raised. These vibrations are often not related to problems with structural integrity, but rather to different aspects of comfort of the residents or workers. The aim of this thesis is to provide additional information regarding the dynamic behavior of hollow core floors. An experimental modal analysis has been performed on an existing floor in an office building. The dynamic properties in the form of natural frequencies, mode shapes, damping ratios and frequency response functions were derived and analyzed from these measurements. Subsequently, several finite element models were developed, aiming to reproduce the experimental dynamic behavior of the studied floor. The measurements initially showed some unexpected dynamic responses of the floor. For this reason, more advanced methods of signal analyses were applied to the data. The analyses showed that the slab has some closely spaced modes and that the modes of the floor are complex to a certain degree. The finite element models were studied with different configurations. In particular, the effect the model size, boundary conditions, material properties and potential structural discontinuities have on the dynamic response of the slab was studied. Sufficiently good agreement has been achieved between the experimental and numerical results in terms of natural frequencies and mode shapes. The acceleration amplitude responses of the numerical models were generally higher than the ones obtained from the measurements, which leads to difficulties in matching of the frequency response functions. Håldäck i betong används idag i stor utsträckning som bjälklag i bostads- och kontorsbyggnader, liksom i parkeringsgarage och köpcentra. Håldäcksbjälklag består av prefabricerade och förspända betongelement, med cylindriska hål som sträcker sig i plattans längsriktning. Dessa konstruktionselement har fördelen, jämfört med platsgjutna betongplattor, att de har en hög hållfasthet på grund av förspänningen och att hålen möjliggör en lägre egenvikt. Dessutom gör hålen att en mindre mängd betongmaterial behövs. Dessa egenskaper ger möjligheter att bygga golv med långa spännvidder och slank design. En konsekvens av slankheten är emellertid att sådana golv har en ökad känslighet för vibrationer som orsakas av olika dynamiska belastningar. I bostads- och kontorsbyggnader orsakas vibrationer främst av mänsklig aktivitet, och därför finns det en del oro relaterad till sådana golvs brukbarhet. Dessa vibrationer är oftast inte relaterade till frågor om strukturell integritet, utan snarare till olika aspekter av boendes eller arbetares känsla av komfort. Syftet med detta examensarbete är att bidra till kunskapen om håldäcksbjälklags dynamiska beteende. En experimentell modalanalys har utförts på ett befintligt golv i en kontorsbyggnad. De dynamiska egenskaperna i form av egenfrekvenser, modformer, dämpning och frekvenssvarsfunktioner erhölls och analyserades med hjälp av dessa mätningar. Därefter utvecklades flera finita element modeller för att reproducera det experimentellt uppmätta dynamiska beteendet hos det studerade golvet. Mätningarna visade initialt något oväntade dynamiska responser från golvet. Av denna anledning applicerades mer avancerade signalanalysmetoder på datan. Analyserna visade att plattan har några moder inom ett litet frekvensintervall och att moderna till en viss grad är komplexa. De finita element modellerna studerades med olika konfigurationer. I synnerhet studerades effekten av modellstorleken, randvillkoren, materialegenskaperna och potentiella strukturella diskontinuiteter på golvets dynamiska respons. Tillräckligt bra överensstämmelse har uppnåtts mellan de experimentella och numeriska resultaten i form av egenfrekvenser och modformer. Accelerationsamplituderna för de numeriska modellerna var i allmänhet högre än de som erhölls under mätningarna, vilket leder till svårigheter att matcha frekvenssvarsfunktionerna.

Simulation data are presented for identifying and analysing the dynamic properties of the rainbow metamaterials as presented in the articles “Rainbow metamaterials for broadband multi-frequency vibration attenuation: numerical analysis and experimental validation” (Meng et al., 2019 [1]) and “Optimal design of rainbow elastic metamaterials” (Meng et al., 2019 [2]). In this data article, the frequency response functions and mode shapes of the rainbow metamaterials are numerically calculated by Finite Element models set up in Ansys Mechanical APDL. Harmonic analysis was performed to figure out the receptance function values of the rainbow metamaterials within the frequency regime 0–500 Hz. Modal analysis was applied to estimate the mode shapes, which could be used to explain the critical peaks and dips in the receptance function curve. Source files of Finite Element models are provided in the data. The Finite Element simulation is not only an effective alternative way to estimate the dynamic properties of the rainbow metamaterials, the mode shape analysis, which is unlikely to be achieved with the analytical model, provides direct insights into the underlying vibration mechanism of the rainbow metamaterials.

This paper presents the design and optimization of a novel MEMS tuning fork gyroscope microstructure. In order to improve the mechanical sensitivity of the gyroscope, much research has been carried out in areas such as mode matching, improving the quality factor, etc. This paper focuses on the analysis of mode shape, and effectively optimizes the decoupling structure and size of the gyroscope. In terms of structural design, the vibration performance of the proposed structure was compared with other typical structures. It was found that slotting in the middle of the base improved the transmission efficiency of Coriolis vibration, and opening arc slots between the tines reduced the working modal order and frequency. In terms of size optimization, the Taguchi method was used to optimize the relevant feature sizes of the gyroscope. Compared with the initial structure, the transmission efficiency of Coriolis vibration of the optimized gyroscope was improved by about 18%, and the working modal frequency was reduced by about 2.7 kHz. Improvement of these two indicators will further improve the mechanical sensitivity of the gyroscope.

The gun head is the end effector of the fire-fighting jet system. Compared with a traditional fixed gun head, an adaptive gun head has the advantages of having an adjustable nozzle opening, a wide applicable flow range, and a high fire-extinguishing efficiency. Thus, the adaptive gun head can extinguish large fires quickly and efficiently. The fire-fighting jet system with an adaptive gun head has fluid-structure interaction and discrete-continuous coupling characteristics, and the influence of key design parameters on its natural frequencies needs to be determined by a sensitivity analysis. In this paper, the dynamic model and equations of the jet system were established based on the lumped parameter method, and the sensitivity calculation formulas of the natural frequency of the jet system to typical design parameters were derived. Natural frequencies and mode shapes of the jet system were determined based on a mode analysis. The variation law of the sensitivity of the natural frequency of the jet system to typical design parameters was revealed by the sensitivity analysis. The results show that the fluid mass inside the spray core within a certain initial gas content is the most important factor affecting the natural frequency of the jet system. There was only a 0.51% error between the value of the first-order natural frequency of the jet system determined by the modal experiment and the theoretical one, showing that good agreement with the first-order natural frequency of the jet system was found. This paper provides a theoretical basis for the dynamic optimization design of the adaptive gun head of the fire water monitor.

The free vibration characteristics, such as fundamental frequency and mode shape of stiffened plates employing standard finite element analysis, are investigated in this paper. The parametric study is presented for free vibration characteristics of stiffened plates with various parameters, such as type, orientation and number of stiffeners, boundary conditions and aspect ratio of plates and stiffener depth to plate thickness ratio. Typical mode shapes are also presented for clamped square eccentrically stiffened plates. Finally, design charts with non-dimensional parameters are proposed to determine the fundamental frequency of commonly adopted clamped stiffened plates in construction. These charts will be very much useful for designers for obtaining the fundamental frequencies of the stiffened plates of different dimensions without doing much complicated analysis or using standard computer codes.

Most of the proposed methods for obtaining the free vibration natural frequency of the retaining wall assume the behavior of the wall in the two-dimensional domain, and they are not able to express the three-dimensional behavior of these structures in a satisfying manner. Moreover, the effect of damping has not yet been considered in analytical study. In this paper, the plate theory and Galerkin method is employed to analyze the free vibration of a wall-reinforcement-soil system in the three dimensional domain and survey the effect of damping on the natural frequency of a retaining wall. So, the retaining wall is modeled as a clamped-free plate and the stiffness of the soil and reinforcements existing behind the wall are modeled as a set of springs and the damping effect of the system is modeled by a set of dampers located at the back of the Retaining wall and attached to it. The results of the proposed model are compared with both the results of the other researchers and the ones from finite element method (FEM). They are also compared with the results of a full-scale experiment and it shows a good agreement. The proposed method which uses the plate theory, also yields the free vibration natural frequencies of the wall’s extensional modes with an acceptable accuracy. Finally, the effect of tensile and compressive behaviors of the soil and the reinforcements on the fundamental frequency of a reinforced retaining wall is studied.

Bu çalışmada grafentabakaların membran gibi modellenerek serbest titreşim analizleri yapılmıştır.Membranlar eğilmeye ya da burkulmaya karşı rijitliği olmayan ince plaklardır.Yanal güçleri eksenel ve merkezi kesme kuvvetleri ile taşırlar. Böyle yüktaşımaları, aşırı incelikleri ve moment taşıma kapasitelerinin ihmal edilebilirolmasından dolayı gergin kablo ağlarına benzetilebilirler. Grafen tabakalardikdörtgen ve kare geometriye sahip olmak üzere değişik boyutlardamodellenmiştir. Elde edilen denklemin çözümünde hem ayrık tekil konvolüsyonyöntemi ve hem de analitik yöntem kullanılmıştır. Literatürde bulunan plakmodeli ile ilk defa yapılan membran modelinin sonuçları karşılaştırılmıştır. Bulunandeğerler grafik ve tablo halinde sunulmuştur., In this present studyvibration analysis of graphene sheets have been carried out by modeling asmembrane model. Membranes are thin plates without the stiffness against bendingand buckling. They carry lateral forces with axial and central shear forces.This specification, its extreme thinness and negligible moment capacity ofmembranes can be likened to the tense cable network. Graphene sheets aremodeled in square and rectangular geometry. The resulting equation have beensolved both analytically and the method of discrete singular convolution. Thefirstly obtained membrane results have been compared with results obtained byplate models in the literature. Results are given in graphics and tables.