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This paper aims to present comprehensive lists of accurate natural frequencies of isotropic thin free rectangular plates constrained only by translational springs distributed uniformly on the edges. Analytical and numerical approaches are employed to study the free vibration of the plates. The first approach is an extension of Ritz method, and second approach is the finite element method coded by the author. Numerical examples cover rectangular plates from totally free plate to totally simply supported on all edges. Convergence and comparison studies are made to establish accuracy of these solutions. Nine numerical examples are presented in terms of different of elastic constraints, and the lowest six frequency parameters are provided in the examples with different aspect ratios.

This paper aims to present comprehensive lists of accurate natural frequencies of isotropic thin free rectangular plates constrained only by translational springs distributed uniformly on the edges. Analytical and numerical approaches are employed to study the free vibration of the plates. The first approach is an extension of Ritz method, and second approach is the finite element method coded by the author. Numerical examples cover rectangular plates from totally free plate to totally simply supported on all edges. Convergence and comparison studies are made to establish accuracy of these solutions. Nine numerical examples are presented in terms of different of elastic constraints, and the lowest six frequency parameters are provided in the examples with different aspect ratios.

Dynamic load analysis of Ultra-High-Performance Concrete (UHPC) beams is crucial, given the material's widespread use in bridges, enabling engineering feats like 100 meter single-span bridges. Structural vibration monitoring aids in evaluating a structure's ability to withstand dynamic loads, employing finite element (FE) model analysis for verification and enhancement. This study utilizes ANSYS for finite element modelling (FEM) and modal analysis, assessing the UHPC beam's structural integrity. An undamaged UHPC beam model validates dynamic properties, reducing disparities between analytical and experimental results. Modal properties of the first cracked and damaged UHPC beam are updated to represent actual conditions. Vibration analysis reveals inherent vibration modes, frequencies, and forms. Structural stiffness analysis verifies the relationship between stiffness and dynamic qualities. Experimental data updates the UHPC beam model, establishing a connection between structural stiffness and natural frequency under various conditions. In conclusion, ANSYS was employed for FEM, modal analysis, and parameterization verification, revealing the importance of accurate UHPC feature identification and meshing size. Discrepancies highlight the need for experimental tests, reducing differences between FEM and empirical findings. The numerical analysis in ANSYS underscores the correlation between structural stiffness and natural frequency, enabling precise structural health monitoring for UHPC beam damage or deterioration identification.

Accurate determination of modal parameters for disk-like structures submerged in heavy fluids is a topic of interest in many fields. For instance, some type of hydraulic turbomachinery can be modelled as disk structures due to the similarity in their mode shapes. Although in the recent years many studies have analyzed and correctly predicted the fluid added mass effect on the natural frequencies and mode shapes of these types of structures, it is particularly challenging to determine fluid damping and characterize its most influential effects. In this article, the influence of vibration amplitude on the fluid damping ratio of a submerged disk, when the disk gets close to a rigid wall, is analytically and experimentally studied. Particularly, the first diametrical modes of the disk have been analyzed at different vibration amplitudes and at very small distances away from a rigid surface. The disk is put in a resonant state by means of a piezoelectric patch generating a harmonic excitation and the response is measured by means of a Laser Doppler Vibrometer (LDV). The damping ratio is obtained directly from the vibrating free decay following a sudden stop of the excitation. It is shown that the fluid damping ratio values are related to the vibration amplitude: there is a trend of increasing damping ratio as the amplitude of the vibration increases. This effect is found to be much larger for small distances between the disk and the rigid surface., Peer Reviewed, Postprint (published version)

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).

Earthquake engineers have taken many precautions in their building designs to protect and minimize destructive effects. In this way, many new design and reinforcement methods have been developed against seismic loads. The use of a tuned mass damper (TMD) is one of the developed methods. One of the most important negative aspects of the use of TMD is the increase in the structural period. Therefore, in this study, the effects of TMD on periods and mode shapes in simeterically reinforced concrete building model were investigated. For this, two models with and without TMD were created by the finite element method and modal parameters were compared. As a result of the data obtained, it has been observed that the building model makes more balanced displacements, as can be understood from the mode shapes, without increasing the period of the building to a dangerous level. It is known that TMD reduces the seismic effect by acting in the opposite direction to the seismic effect on the structure. Tuned mass damper can be used in structures, provided that it does not increase the structure period too much.

Earthquake engineers have taken many precautions in their building designs to protect and minimize destructive effects. In this way, many new design and reinforcement methods have been developed against seismic loads. The use of an active mass damper (AMD) is one of the developed methods. One of the most important negative aspects of the use of AMD is the increase in the structural period. Therefore, in this study, the effects of AMD on periods and mode shapes in symmetrically reinforced concrete building model were investigated. For this, two models with and without AMD were created by the finite element method and modal parameters were compared. As a result of the data obtained, it has been observed that the RC building model makes more balanced displacements, as can be understood from the mode shapes, without increasing the period of the RC building to a dangerous level. It is known that AMD reduces the seismic effect by acting in the opposite direction to the seismic effect on the structure. Active mass damper can be used in reinforced concrete buildings, provided that it does not increase period too much.

Earthquake engineers have taken many precautions in their building designs to protect and minimize destructive effects. In this way, many new design and reinforcement methods have been developed against seismic loads. The use of a pendulum tuned mass damper (PTMD) is one of the developed methods. One of the most important negative aspects of the use of PTMD is the increase in the structural period. Therefore, in this study, the effects of PTMD on periods and mode shapes in symmetrically reinforced concrete water tank model were investigated. For this, two models with and without PTMD were created by the finite element method and modal parameters were compared. As a result of the data obtained, it has been observed that the water tank model makes more balanced displacements, as can be understood from the mode shapes, without increasing the period of the water tank to a dangerous level. It is known that PTMD reduces the seismic effect by acting in the opposite direction to the seismic effect on the structure. Pendulum tuned mass damper can be used in reinforced concrete water tanks, provided that it does not increase period too much.

Use of Sandwich construction for an aircraft structural component is very common to the present day. One of the primary requirements of aerospace structural materials is that they should have low density, very stiff and strong. Sandwich panels are thin-walled structures fabricated from two flat sheets separated by a low density core. We have investigated here is of aluminium honeycomb structure because of excellent crush strength and fatigue resistance. Sandwich panels have a very high stiffness to weight ratio with respect equivalent solid plate because of low density core. FEA modeling is developed by consideration of rotary inertia. The free vibration analysis of sandwich panels is studied. Four noded isoparametric shell element is used for FEA. The effects of sandwich design parameters, such as face thickness, core thickness and pitch, on the global bending and vibration responses are determined. Convergence study is also included for high accuracy of the results. Analytical results are based on classical bending theory. Mode shapes and corresponding natural frequencies are studied for simply supported sandwich panel and cantilever condition.

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

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.

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.

The timber concrete composite (TCC) deck system is a new technology that consists of timber and concrete composite structures but remains uncommon in Malaysia. TCC is a structural system where timber beams and concrete slabs are combined to form a composite material, resisting tensile stress and compressive stress, respectively. The addition of concrete slabs protects timber beams from direct contact with water, which is crucial to ensure the durability of timber beams. Different types of connectors can be used to provide force exchange between concrete slabs and timber beams. This research was conducted to study the vibration behavior of timber-concrete composite deck systems with or without concrete topping. The deck was constructed using twenty pieces of sawn timber measuring 3.6m x 0.09 m with a concrete topping of 0.065m. Experimental tests were conducted using an electrodynamic shaker with a frequency range of 1 Hz to 200 Hz. The shaker was placed on a laminated deck as vertical force and 15 accelerometers were used as output data collectors. Me´scope and SAP2000 package were used for data analysis. The natural frequency values of the first mode shape with and without concrete topping based on Me´scope analysis are 12.8Hz and 16.9Hz, respectively. Meanwhile, the finite element modeling analysis shows that the frequency of the first mode shape with laminated deck without concrete topping is 11.4 Hz while the one with concrete topping is 16.2 Hz. The natural frequencies obtained from the experimental test and the modal analysis are greater than 8 Hz, thereby concluding that the TCC laminated deck system is suitable and comfortable for building occupants.

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 co, 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 struktu

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., Aerospace Structures & Computational Mechanics

Micromechanical Thermal Analysis utilizes microstring resonators to analyze a minimum amount of sample to obtain both the thermal and mechanical responses of the sample during a heating ramp. We introduce a modulated setup by superimposing a sinusoidal heating on the linear heating and implementing a post-measurement data deconvolution process. This setup is utilized to take a closer look at the glass transition as an important fundamental feature of amorphous matter with relations to the processing and physical stability of small molecule drugs. With an additionally developed image and qualitative mode shape analysis, we are able to separate distinct features of the glass transition process and explain a previously observed two-fold change in resonance frequency. The results from this setup indicate the detection of initial relaxation to viscous flow onset as well as differences in mode responsivity and possible changes in the primary resonance mode of the string resonators. The modulated setup is helpful to distinguish these processes during the glass transition with varying responses in the frequency and quality factor domain and offers a more robust way to detect the glass transition compared to previously developed methods. Furthermore, practical and theoretical considerations are discussed when performing measurements on string resonators (and comparable emerging analytical techniques) for physicochemical characterization.

Application of irregular mass configuration in modern design era of buildings is unavoidable in order to serve various building functionality. Discontinued and unsymmetrical mass applied on a structure could vary its dynamic behaviour. Thus, a regular geometry of 5-storey steel frame tower at 5 meter height is designed and constructed in Jamilus Research Centre laboratory, to investigate the dynamic characteristics in terms of natural frequencies and its mode shapes subjected to various mass orientations. A total of four steel blocks at 800 kg are placed in equivalent, ascending and alternating orientations on the 1st to 4th storey of the frame. Ambient vibration (AV) technique is used for dynamic characteristics evaluation. Uni-axial accelerometer sensors are aligned in bi-axial horizontal directions of North-South and East-West. ARTeMIS processing tool and Frequency Domain Decomposition (FDD) methods are used for modal parameters determination. Comparative findings are made between bare frame and mass action frame. Significant reduction of predominant frequency showed up to 37.79% between bare frame against frame in ascending mass orientation. Equivalent mass orientation shows the lowest percentage discrepancy percentage compared to others. Two translation mode shapes and torsional mode are illustrated by respective three predominant frequencies. Even though some changes have be found in predominant frequencies, but comparable mode shapes illustration are observed from all three frequency modes from all frame configurations.

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., Peer Reviewed, Postprint (author's final draft)

[EU] Dokumentu honetan balazta baten diskoaren analisi modal teorikoa eta esperimentala konparatzen dira. Analisi teorikoa elementu finituen metodoa erabiliz egin da ANSYS softwareari esker. Korrelazioa egiteko, berriz, BK Connect programa baliatu da, zeinetan aurretiaz egindako analisi esperimentaleko emaitzak dauden. Hortaz, ANSYS eta BK Connect-en arteko konexio hori ahalbidetzeko datu teoriko guztiak formatu unibertsalean idazten dituen programa bat garatu zen Fortran programazio lengoaian. Honi esker, emaitza teorikoak BK Connect-ek ireki dezakeen zenbait fitxategi sortu dira analisi esperimentalarekin lortutakoekin konparatu direnak. Izan ere, analisi esperimentaleko emaitzak zuzenak diren balioztatzeko Modal Assurance Criterion (MAC) deritzon korrelazio metodoa erabili da eta emaitzak grafikoki ere adierazi dira., [ES] En este documento se ha llevado a cabo la comparación teórica y experimental del análisis modal del disco de un freno. Para ello, haciendo uso del software ANSYS se ha hecho el análisis teórico utilizando el método de elementos finitos. Dicha correlación se ha llevado a cabo mediante el programa BK Connect, en el cual está guardado el análisis experimental previamente realizado. Por consiguiente, para posibilitar la conexión entre ambos, se ha desarrollado un programa mediante el lenguaje Fortran, el cual transforma los datos teóricos en formato universal. Así, se han creado varios archivos que pueden ser abiertos por BK Connect y que se han comparado con los datos experimentales. De hecho, para la validación de los datos experimentales se han comparado los datos mediante el llamado Modal Assurance Criterion (MAC)., [EN] In this document a comparison between the experimental and theoretical modal analysis of a disc of a brake is carried out. In order to do the theoretical analysis, the Finite Element Method have been used thanks to the software ANSYS. On the other hand, the program BK Connect has been used to make the correlation where the results obtained from experimental modal analysis are saved. Therefore, to make the connection between those two programs possible, a new program has been developed with Fortran, which creates some files with universal format. These files can be opened by BK Connect, so that the comparison with the experimental analysis can be done. In fact, using the Modal Assurance Criterion (MAC) the correlation has been made and the results have been represented in a graphic.

When simulating the vibration behaviour of large 2-stroke marine diesel engines the damping properties are an important parameter to be considered. Simulations only allow determining realistic vibration amplitudes if the engine’s damping characteristic is known. Modal damping ratios of reciprocating engines vary depending on which parts of the engine interact during oscillation and on how energy is dissipated while vibrating. Therefore different damping ratios can be expected for different engine mode shapes. For determining typical modal damping ratios of a diesel engine a methodology for an automated analysis of vibration measurement data was developed: After identifying N resonance peaks in a measured vibration spectrum a spectral curve corresponding to a simple mass-spring-damper system with N degrees of freedom is automatically fitted onto the measured curve by parameter optimization. At the end of this iterative process the damping properties of the substituting mass-spring-damper-system, whose curve adjusts most precisely to the measured spectrum, are attributed to the measured resonances. In addition to determining modal damping ratios and eigenfrequencies the procedure allows separating overlapping resonance peaks. The analysis process was applied on vibration measurement results of a series of different marine diesel engines and characteristic modal damping ratios could be determined for the engine’s principal mode shapes. Considering the determined modal damping properties when performing forced response simulations of the engine by modal superposition in the frequency domain allowed to achieve a higher accuracy in the calculated vibration amplitudes.

During flight, insect wings bend and twist under the influence of aerodynamic and inertial forces. We tested whether wing resonance of honeybees (Apis mellifera) matches the wingbeat frequency, against the 'stiff element' hypothesis that the wing's first longitudinal mode exceeds the wingbeat frequency. Six bees were immobilized with their right wing pair outspread, and stimulated with a shaker while the normal modes were recorded with a scanning Doppler laser vibrometer. The lowest normal mode of the wings was the first longitudinal bending mode and, at 602±145 Hz, was greater than the wingbeat frequency of 234±13.9 Hz. Higher-order normal modes of the wing tended to incorporate nodal lines in the chordwise direction of the trailing edge, suggesting that their mode shape did not strongly resemble wing deformation during flapping flight. These results support the stiff element hypothesis for Apis mellifera.

In many areas of engineering such as telecommunications industry, lenses and optical cooling, waveguiding and the ability to control wave propagation is necessary. Phononic Crystals (PnCs) influence the propagation of mechanical waves by their periodic variation in elastic impedances. Depending on Lattice type and inclusion's spacing, one can manipulate the frequencies that are blocked or allowed to transmit through the crystal in a particular direction. In this work, two dimensional PnCs plates are design and also numerically and experimentally demonstrated. Finite Element Analysis (FEA) was performed to study the dispersion behavior and eigenmodes of a PnC. The simulations show the existence of a complete bandgap, thus acoustic PnC devices such as cavity, resonator and waveguide are created accordingly by introducing a line defect to the crystal. The experimental response of the devices was then measured by fabricating and then testing them. These results show excellent agreement with the FEA. For the first time waveguide and 90áµ’ bend is designed that have several isolated modes in the bandgap with transmission efficiencies above 90% for a specific frequency range. In this seminar also a few novel patents will be introduced. We consider a two-dimensional periodic square array of the air holes in a finite aluminum medium. The defect introduced to the crystals are acting as local acoustic resonances/guiding with the substrate and lead to the possibility of finding a low-frequency confined acoustic waves or guided modes. Studying the mode shapes will help to shed light on the origin of BG formation and as the results BG optimization. The numerical and experimental results presented here are related to the case of Aluminum-air devices, but the conclusions remain valid for other materials and compositions as well.

A task is decided about the vibrations of round plate of arcwise-variable thickness by the method of symmetries. Frequency equalizations over and equalizations of forms of native are brought. The analysis of the tensely-deformed state of plate of variable thickness is executed. The chart of estimation of longevity and operating resource of plate is offered at her possible using as an active acoustic element of resonant devices.Reference 7, figures 5, tables 1., Решена задача о колебаниях круглой пластинки линейно-переменной толщины методом симметрий. Приведены частотные уравнения и уравнения форм собственных колебаний. Выполнен анализ напряженно-деформированного состояния пластинки переменной толщины. Предложена схема оценки долговечности и эксплуатационного ресурса пластинки при ее возможном использовании в качестве активного акустического элемента резонансных устройств.Библ. 7, рис. 5, табл. 1., Розв’язано задачу про коливання круглої пластинки з лінійним законом зміни товщини на основі використання методу симетрій. Наведено частотні рівняння та рівняння форм власних коливань. Виконано аналіз напружено-деформованого стану пластинки змінної товщини. Запропоновано схему оцінки довговічності та експлуатаційного ресурсу пластинки за умови її можливого використання в якості активного акустичного елементу резонансних пристроїв.Бібл. 7, рис. 5, табл. 1.

Identification of modal parameters from output-only data is studied in this work. The proposed methodology uses transmissibility functions obtained under different loading conditions to identify resonances and mode shapes. The technique is demonstrated with numerical simulations on a 2-DOF system and a cantilever beam. To underpin the simulations, a real test was done on a beam to show the efficiency of the method. A practical application of the method can be to identify structures subjected to moving loads. This is demonstrated by using FEM-model of a cantilever beam with a moving load., Operational Modal Analysis (OMA) is being increasingly used as an experimental technique to identify the dynamic properties of many types of large-scale constructed systems. For industrial structures in real operation condition, it is sometimes hard or impossible to measure excitation forces so some identification techniques have been developed to work on response data only. In Operational Modal Analysis (OMA), there is no need to make any assumption about the nature of force and consequently resonance frequencies are recognised. In this thesis, one application of Operational Modal Analysis which is called transmissibility measurement is supposed to be engaged to find resonance frequencies. Operational Modal Analysis has become a valid alternative for structures where a classic forced-vibration test would be difficult to conduct. The use of in-operation modal analysis is particularly interesting because the structure remains in its normal in-operating condition during the test. This is an important advantage because the conditions during a laboratory forced-vibration test are often considerably different from the real working conditions regardless of constraints and limitations. Therefore, this method enables us to find system parameters without any assumption about the nature of the forces., Phone : +46704997666 E-mail : amirhossein.aghdasi@hotmail.com

Slab–girder structures composed of steel girder and reinforced concrete slab are widely used in buildingsand bridges in the world. Their advantages are largely based on the composite action through the shear connection between slab and girder. In order to assess the integrity of this kind of structures, numerous vibration-based damage identification methods have been proposed. In this study, a scaled composite slab–girder model was constructed in the laboratory. Some removable shear connectors were speciallydesigned and fabricated to connect the girder and slab that were cast separately. Then, a two-stage experiment including both static and vibration tests was performed. In the first stage, vibration tests were conducted under different damage scenarios, where a certain number of shear connectors at certain locations were removed step by step. In the second stage, two sets of hydraulic loading equipment were used to apply four-point static loads in the test. The loads are increased gradually until concrete slabcracked. The loading histories as well as deflections at different points of the beam are recorded. Vibration test was carried out before and after concrete cracking. Experimental results show that the changes of mode shapes and relative displacement between slab and girder may be two promising parameters for damage identification of slab–girder structures.

The analysis of the dynamic response of a vibrating structure in contact with a fluid medium can be interpreted as an added mass effect known as the Fluid Structure Interaction (FSI) problem. This effect is critical in the study of composites for marine applications since the densities of the composites and water are relatively close to one another. In this study, experimental testing was conducted to compare the free vibration response of composite beams in air with those in FSI immersed in water. Composite beams with six layers of non-biased, plain weave, 6 oz E-glass were used with two different layer orientations and boundary conditions. Five samples were layered at the 0 and 90 degree orientations and five samples were layered at the plus and minus 45 degree orientation. The Digital Image Correlation (DIC) technique was used to test each of the ten samples in a cantilever boundary condition with an initial displacement to induce a free vibration response both in air and immerse in water. A High Speed Camera (HSC) was also used to gain further frequency information during each of these tests. A second set of two composite beams were constructed with 16 layers at both of the described orientations. These were instrumented with accelerometers to conduct a modal analysis from an impact hammer test. These tests were conducted with the beams in a free-free boundary condition while in air and immersed in water. Prior to conducting these tests, an aluminum beam was tested with the same conditions to verify the waterproofing of the accelerometers and to ensure valid data was collected. The findings of this study will provide a better understanding for the use of composite materials in marine applications where various excitations can occur.

The study presents a multi-layer genetic algorithm (GA) approach using correlation-based methods to facilitate damage determination for through-truss bridge structures. To begin, the structure’s damage-suspicious elements are divided into several groups. In the first GA layer, the damage is initially optimised for all groups using correlation objective function. In the second layer, the groups are combined to larger groups and the optimisation starts over at the normalised point of the first layer result. Then the identification process repeats until reaching the final layer where one group includes all structural elements and only minor optimisations are required to fine tune the final result. Several damage scenarios on a complicated through-truss bridge example are nominated to address the proposed approach’s effectiveness. Structural modal strain energy has been employed as the variable vector in the correlation function for damage determination. Simulations and comparison with the traditional single-layer optimisation shows that the proposed approach is efficient and feasible for complicated truss bridge structures when the measurement noise is taken into account.

The present study aims at investigating the potential of using mode shape or mode shape curvature (MSC) for detecting defects in wooden beams. It includes modal analysis, Finite Element (FE) modeling and visual scanning. An FE model was created to investigate the effect of defects of different size and location on the mode shape/MSC. The mode shape/MSC showed a good potential to be used for finding defects. An experimental study on 17 boards of Norway spruce, dimensions of 50×150×3900 mm, was conducted using experimental modal analysis. The findings reveal that: (1) the mode shape/MSC studied in the FE-model could be used to locate defects, (2) the method is very sensitive to measurement noise and it requires an accurately measured mode shape, (3) an error analysis shows that it is not possible to achieve the accuracy needed using accelerometers.

In the present work the change in natural frequencies, damping and mode shapes of a prefabricated timber floor element have been investigated when it was integrated into a building structure. The timber floor element was first subjected to modal testing in laboratory with ungrounded and simply supported boundary conditions, and then in situ at different stages of building construction. The first five natural frequencies, damping ratios and mode shapes of the floor element and the entire floor were extracted and analysed. It may be concluded that the major change in natural frequencies occur as the floor element is coupled to the adjacent elements and when partitions are built in the studied room, the largest effect is on those modes of vibration that largely are constrained in their movement. The in situ conditions have a great influence on the damping, which depends on the damping characteristics of the supports, but also on the fact that the floor is integrated into the building and interacts with it. There is a slight increase of damping in the floor over the different construction stages and the damping values seem to decrease with ascending mode order.

This master thesis has been carried out on behalf of Volvo Construction Equipment. A front frame of an articulated hauler should be analysed according to the Finite Element Method and vibration tests should be made. The results from the experimental tests should be correlated with the analytical test results here using MAC-values. These values will show if the FE-model represents the physical structure correctly. Visualisations are made on both the experimental and analytical results to get a better understanding about the eigenmodes of the frame. The final results showed that the FE-model was not a match to the physical structure which the experimental tests were made on. It should be noted that the final result only states the present situation. The CAD-model had not been completed when this thesis was performed and therefore some deviation occurred in the results. Some actions are needed in order to reach a better result and they are stated in this report. When they are made, the results can be improved by following the work that has been done in this master thesis.

This is the second of three companion papers that examine the elastic buckling andcollapse of laser-welded sandwich panels with an adhesively bonded core and uni-directionalvertical webs. In the first paper, it has been shown that the critical load in compression parallelto the webs can be accurately predicted by using a Pasternak foundation to model the coreand by using a simple clamping factor to describe the boundary conditions at the laser weld.In this paper, the same model is adapted to predict the critical load in compression normal tothe webs. As the face plate is now short and wide, rather than long and narrow as before, a‘constrained wrinkling’ approach is outlined that recognises that the face plate is limited in itsability to wrinkle naturally and can only deform in certain mode shapes. The clamping factorand the effective wave length are derived for different buckling mode shapes and boundaryconditions at the laser weld, and the constrained wrinkling load is determined by evaluatingthe buckling load for successive modes and simply picking the smallest value. It is shown that,for low modulus core materials, the constrained wrinkling load is equal to the bare platebuckling load and, for high modulus materials, the solution converges toward anti-symmetricalwrinkling, as has been found for the case of compression parallel to webs. The constrainedwrinkling load agrees well with finite element results but as before the proportional limit ofthe face plate material is usually reached well before elastic buckling occurs., QC 20111220

The presented research examined three areas: best practices in high quality dynamic testing of in-situ floor systems, extensive dynamic testing of three bare (non-fit out) in-situ multi-bay steel composite floors to estimate their dynamic parameters/response and to identify trends in dynamic behavior, and development of a set of fundamental finite element (FE) modeling techniques to adequately represent the dynamic response of steel composite floors for the purpose of evaluating vibration serviceability. The measurement, analysis, and computation of a floor's accelerance frequency response function (FRF) is the core premise linking all areas of the presented research. The burst chirp signal using an electrodynamic shaker is recommended as the most accurate and consistent source of excitation for acquiring high quality measurements suitable for use in parameter estimation, operating deflection shape animation, and calibration/validation of FE models. A reduced mid-bay testing scheme is recommended as a time-saving alternative to modal testing over a full coverage area, provided the only desired estimated parameters are frequencies, damping, and mid-bay acceleration response. Accelerance FRFs were measured with an electrodynamic shaker located within 23 unique bays on the three tested floors. Dominant frequencies ranged from 4.85 Hz to 9 Hz and measured estimates of damping varied considerably, ranging from 0.44% to 2.4% of critical (0.5%-1.15% was typical). Testing showed several mode shapes were localized to just a few bays and not all modes were adequately excited by forcing at a single location. The quality of the estimated mode shapes was significantly improved using multi-reference modal testing. FE models for the tested floors were developed based on high quality measured data and were shown to provide adequate representations of measured floor behavior. Fundamental techniques are presented for modeling mass, stiffness, boundary conditions, and performing dynam

The purpose of this study was to examine the effect of bottom chord extensions on deflections and vibration characteristics of joist supported floor systems when joist bottom chord extensions are installed. To understand the effect of bottom chord extensions on deflections, natural frequency, damping, mode shape and effective mass, extensive analytical and experimental studies were conducted on single span and three span joist supported laboratory footbridges with different bottom chord extension configurations. Finite element computer models were created to simulate and compare the results of stiffness and vibration tests. Testing was done with a) the bottom chord extensions in-place before the concrete was placed, b) with all or part of the bottom chord extensions removed, and c) after the bottom chord extensions had been reinstalled with jacking for the single span footbridge and without jacking for the three-span footbridge. Results from the stiffness tests indicate that re-installing the bottom chord extensions to the joists of the single span footbridge with cured concrete with the center of the span raised helps to reduce the uniform load deflections to some extent, but not as much as placing the bottom chord extensions before the concrete placement. Likewise, for the three span footbridge, placing the bottom chord extensions before the concrete placement is observed to be a better solution. Results from the dynamic tests indicate that the effect of bottom chord extensions on the single span footbridge is consistent for natural frequency, 20 psf live load deflections, sinusoidal excitations with high amplitudes, quarter point heel drop excitations, walking excitations, and effective mass values. The effect of bottom chord extensions on the three span footbridge is consistent for the natural frequency and 20 psf deflections. However, the FRF (Frequency Response Function) peaks of chirp, heel drop, sinusoidal excitations, accelerations from walking data, and th

This paper presents an analysis of the coupled vibration of asymmetric core structures in tall buildings. The governing equation of free vibration and its corresponding eigenvalue problem, which is a set of equations for laterally flexural vibrations in two different directions coupled by a warping-St. Venant torsional vibration, are derived. Based on the Calerkin method, a generalized approximate method is developed for the analysis of coupled vibration and thus proposed for determining the natural frequencies and mode shapes of the structure in triply-coupled vibration. The results of the proposed method for the example structure show good agreement with those of the FEM analysis. The proposed method has been shown to provide a simple and rapid, yet accurate, means for coupled vibration analysis of core structures.

The lightening of the car-body mass of railway vehicles is desirable for increasing speed and saving energy. But this may adversely affects riding comfort due to increased bending vibration of the car-body. so, in order to examine the bending vibration characteristics more accurately, it was necessary to improve the calculation model. The improved model for vertical bending is a uniform beam supported on 2 resilient stands at each truck center position. Calculation results about mode shapes and natural frequencies are compared with the bench test data of a real car. As a result, it was made clear that the bending mode remarkable in real cars was simulated more accurately by the 2nd modal shape of an elastically supported beam. And, in the range of the realistic value of supporting elasticity, this shape almost corresponds with the 1 st modal one of free beam.

Předmětem diplomové práce je porovnání výsledků modální analýzy desek plošných spojů bez elektronických komponent, které byly získány při výpočtovém a experimentálním modelováním. Analýzy jsou provedeny pro varianty jednovrstvé a následně třívrstvé PCB. Běžně jsou desky uchyceny za delší strany pomocí klínového zámku. Aby bylo možné realizovat okrajové podmínky ve výpočtovém i experimentálním modelování, je reálné upnutí PCB zjednodušeno na zamezení posuvů. Výpočtové modely jsou vytvořeny pomocí MKP prvků, které se běžně využívají pro řešení problémů tohoto typu. Stanovené výsledky jsou porovnány s výsledky experimentálního modelování. V práci je také otestována citlivost modelů na změnu velikosti prvku a počet prvků po tloušťce., Modal analysis of printed circuit board results, gained from computional and experimental modeling, have been compared. Anylyses have been performed on dummy boards (models without electronic components), created as one-layered at first, then as three-layered PCB. Board is usually clamped by its longer edges with wedgelock. In order to enable the realization of boundary conditions in computional and experimental modeling, real clamping has been simplified to simply supported. Computional models have used FEM elements, which are comomnly used in this type of problem. Determined results have been evaluated by comparing the experimental modeling results. Models‘ sensitivity on modification of element length and number of elements through thickness have been performed.

Vplyvom prostredia sa menia dynamické vlastnosti telesa. Táto práca sa zapodieva expe-rimentálnym preukázaním tohto javu. Cieľom je určenie vlastných frekvencií voľne visiaceho telesa budeného rázom na vzduchu a vo vode a ich vzájomné porovnanie. Skúmané teleso je rúra, ktorá bola v rámci experimentu skracovaná. V práci je tiež pozorovaný vplyv zmeny geometrie na vlastné frekvencie a vlastné tvary telesa. Výsledky experimentálnej modálnej analýzy sú porovnané s výpočtom vykonaným v softvéri ANSYS., The dynamic characteristics of the object are influenced by the changes of the envi-ronment. The objective of this report is to examine how the changes of the environment influ-ence the dynamic characteristics of the object. The main aim is to compare the natural fre-quencies of the object when suspended and then actuated when being surrounded by air and submerged in water. The object in question is a cylindrical pipe, which was gradually short-ened during the experiment. These changes in size also affected the natural frequencies and the mode shape, which is discussed as well. The results of the experimental modal analysis are compared to calculations run in ANSYS software.

Vplyvom prostredia sa menia dynamické vlastnosti telesa. Táto práca sa zapodieva expe-rimentálnym preukázaním tohto javu. Cieľom je určenie vlastných frekvencií voľne visiaceho telesa budeného rázom na vzduchu a vo vode a ich vzájomné porovnanie. Skúmané teleso je rúra, ktorá bola v rámci experimentu skracovaná. V práci je tiež pozorovaný vplyv zmeny geometrie na vlastné frekvencie a vlastné tvary telesa. Výsledky experimentálnej modálnej analýzy sú porovnané s výpočtom vykonaným v softvéri ANSYS., The dynamic characteristics of the object are influenced by the changes of the envi-ronment. The objective of this report is to examine how the changes of the environment influ-ence the dynamic characteristics of the object. The main aim is to compare the natural fre-quencies of the object when suspended and then actuated when being surrounded by air and submerged in water. The object in question is a cylindrical pipe, which was gradually short-ened during the experiment. These changes in size also affected the natural frequencies and the mode shape, which is discussed as well. The results of the experimental modal analysis are compared to calculations run in ANSYS software.

The analysis of the dynamic response of a vibrating structure in contact with a fluid medium can be interpreted as an added mass effect known as the Fluid Structure Interaction (FSI) problem. This effect is critical in the study of composites for marine applications since the densities of the composites and water are relatively close to one another. In this study, experimental testing was conducted to compare the free vibration response of composite beams in air with those in FSI immersed in water. Composite beams with six layers of non-biased, plain weave, 6 oz E-glass were used with two different layer orientations and boundary conditions. Five samples were layered at the 0 and 90 degree orientations and five samples were layered at the plus and minus 45 degree orientation. The Digital Image Correlation (DIC) technique was used to test each of the ten samples in a cantilever boundary condition with an initial displacement to induce a free vibration response both in air and immerse in water. A High Speed Camera (HSC) was also used to gain further frequency information during each of these tests. A second set of two composite beams were constructed with 16 layers at both of the described orientations. These were instrumented with accelerometers to conduct a modal analysis from an impact hammer test. These tests were conducted with the beams in a free-free boundary condition while in air and immersed in water. Prior to conducting these tests, an aluminum beam was tested with the same conditions to verify the waterproofing of the accelerometers and to ensure valid data was collected. The findings of this study will provide a better understanding for the use of composite materials in marine applications where various excitations can occur., http://archive.org/details/freevibrationres1094517443, Lieutenant, United States Navy, Approved for public release; distribution is unlimited.

Předmětem diplomové práce je porovnání výsledků modální analýzy desek plošných spojů bez elektronických komponent, které byly získány při výpočtovém a experimentálním modelováním. Analýzy jsou provedeny pro varianty jednovrstvé a následně třívrstvé PCB. Běžně jsou desky uchyceny za delší strany pomocí klínového zámku. Aby bylo možné realizovat okrajové podmínky ve výpočtovém i experimentálním modelování, je reálné upnutí PCB zjednodušeno na zamezení posuvů. Výpočtové modely jsou vytvořeny pomocí MKP prvků, které se běžně využívají pro řešení problémů tohoto typu. Stanovené výsledky jsou porovnány s výsledky experimentálního modelování. V práci je také otestována citlivost modelů na změnu velikosti prvku a počet prvků po tloušťce., Modal analysis of printed circuit board results, gained from computional and experimental modeling, have been compared. Anylyses have been performed on dummy boards (models without electronic components), created as one-layered at first, then as three-layered PCB. Board is usually clamped by its longer edges with wedgelock. In order to enable the realization of boundary conditions in computional and experimental modeling, real clamping has been simplified to simply supported. Computional models have used FEM elements, which are comomnly used in this type of problem. Determined results have been evaluated by comparing the experimental modeling results. Models‘ sensitivity on modification of element length and number of elements through thickness have been performed.

Problematika, kterou řeší tato diplomová práce, se vztahuje k modelování vysokofrekvenčních tlakových pulsací v hydraulických strojích. Pulsace jsou způsobeny vzájemnou interakcí statorových a rotorových lopatek. Jejich působením jsou následně cyklicky namáhány víko, spirála a rozváděcí a oběžné kolo. Matematický model je řešen pomocí přenosových matic. Data jsou vypočtena a zpracována v programech F-A char a MS Excel. Výsledky jsou znázorněny formou frekvenčně amplitudových charakteristik a dále formou tvaru kmitu tlaku, kde je znázorněno i porovnání matematického modelu s měřením., The diploma thesis deals with the mathematical modeling of high-frequency pressure pulsations in water turbines. Pulsations are caused by the interaction between stator a rotor blades. These high-frequency pressure pulsations then cause high cycle fatigue of the head cover, spiral casing, runner and distributor. The mathematical model is solved by transfer matrix method. Data are processed in F-A char and MS Excel programs. Final results are demonstrated by frequency amplitude characteristics and by pressure mode shapes, where comparison of the mathematical model with the measurement is shown.

V analýze tvarů a frekvencí módu vzduchu uzavřeného v kabině automobilu budeme sledovat podstatu měřených veličin, u jednoduchém vnitřního prostoru popíšeme rozdílnost analytického a MKP řešení. Dále vypočteme frekvence a vlastní tvary kmitání vzduchu v kabině automobilu čtyř odlišných karoserií a možnosti ovlivnění frekvencí u jedné z nich., In analysis of natural frequencies and mode shapes of car cabin we shall investigate principle of measured values, we shall describe diferencies between analytic and FEM solution of simplified inside space. In next case we shall compute frequencies and mode shapes of sound inside car cabin of four different body and option of interference by one of them.

Vplyvom prostredia sa menia dynamické vlastnosti telesa. Táto práca sa zapodieva expe-rimentálnym preukázaním tohto javu. Cieľom je určenie vlastných frekvencií voľne visiaceho telesa budeného rázom na vzduchu a vo vode a ich vzájomné porovnanie. Skúmané teleso je rúra, ktorá bola v rámci experimentu skracovaná. V práci je tiež pozorovaný vplyv zmeny geometrie na vlastné frekvencie a vlastné tvary telesa. Výsledky experimentálnej modálnej analýzy sú porovnané s výpočtom vykonaným v softvéri ANSYS., The dynamic characteristics of the object are influenced by the changes of the envi-ronment. The objective of this report is to examine how the changes of the environment influ-ence the dynamic characteristics of the object. The main aim is to compare the natural fre-quencies of the object when suspended and then actuated when being surrounded by air and submerged in water. The object in question is a cylindrical pipe, which was gradually short-ened during the experiment. These changes in size also affected the natural frequencies and the mode shape, which is discussed as well. The results of the experimental modal analysis are compared to calculations run in ANSYS software.

V analýze tvarů a frekvencí módu vzduchu uzavřeného v kabině automobilu budeme sledovat podstatu měřených veličin, u jednoduchém vnitřního prostoru popíšeme rozdílnost analytického a MKP řešení. Dále vypočteme frekvence a vlastní tvary kmitání vzduchu v kabině automobilu čtyř odlišných karoserií a možnosti ovlivnění frekvencí u jedné z nich., In analysis of natural frequencies and mode shapes of car cabin we shall investigate principle of measured values, we shall describe diferencies between analytic and FEM solution of simplified inside space. In next case we shall compute frequencies and mode shapes of sound inside car cabin of four different body and option of interference by one of them.

Předmětem diplomové práce je porovnání výsledků modální analýzy desek plošných spojů bez elektronických komponent, které byly získány při výpočtovém a experimentálním modelováním. Analýzy jsou provedeny pro varianty jednovrstvé a následně třívrstvé PCB. Běžně jsou desky uchyceny za delší strany pomocí klínového zámku. Aby bylo možné realizovat okrajové podmínky ve výpočtovém i experimentálním modelování, je reálné upnutí PCB zjednodušeno na zamezení posuvů. Výpočtové modely jsou vytvořeny pomocí MKP prvků, které se běžně využívají pro řešení problémů tohoto typu. Stanovené výsledky jsou porovnány s výsledky experimentálního modelování. V práci je také otestována citlivost modelů na změnu velikosti prvku a počet prvků po tloušťce., Modal analysis of printed circuit board results, gained from computional and experimental modeling, have been compared. Anylyses have been performed on dummy boards (models without electronic components), created as one-layered at first, then as three-layered PCB. Board is usually clamped by its longer edges with wedgelock. In order to enable the realization of boundary conditions in computional and experimental modeling, real clamping has been simplified to simply supported. Computional models have used FEM elements, which are comomnly used in this type of problem. Determined results have been evaluated by comparing the experimental modeling results. Models‘ sensitivity on modification of element length and number of elements through thickness have been performed.

Problematika, kterou řeší tato diplomová práce, se vztahuje k modelování vysokofrekvenčních tlakových pulsací v hydraulických strojích. Pulsace jsou způsobeny vzájemnou interakcí statorových a rotorových lopatek. Jejich působením jsou následně cyklicky namáhány víko, spirála a rozváděcí a oběžné kolo. Matematický model je řešen pomocí přenosových matic. Data jsou vypočtena a zpracována v programech F-A char a MS Excel. Výsledky jsou znázorněny formou frekvenčně amplitudových charakteristik a dále formou tvaru kmitu tlaku, kde je znázorněno i porovnání matematického modelu s měřením., The diploma thesis deals with the mathematical modeling of high-frequency pressure pulsations in water turbines. Pulsations are caused by the interaction between stator a rotor blades. These high-frequency pressure pulsations then cause high cycle fatigue of the head cover, spiral casing, runner and distributor. The mathematical model is solved by transfer matrix method. Data are processed in F-A char and MS Excel programs. Final results are demonstrated by frequency amplitude characteristics and by pressure mode shapes, where comparison of the mathematical model with the measurement is shown.

Předmětem diplomové práce je porovnání výsledků modální analýzy desek plošných spojů bez elektronických komponent, které byly získány při výpočtovém a experimentálním modelováním. Analýzy jsou provedeny pro varianty jednovrstvé a následně třívrstvé PCB. Běžně jsou desky uchyceny za delší strany pomocí klínového zámku. Aby bylo možné realizovat okrajové podmínky ve výpočtovém i experimentálním modelování, je reálné upnutí PCB zjednodušeno na zamezení posuvů. Výpočtové modely jsou vytvořeny pomocí MKP prvků, které se běžně využívají pro řešení problémů tohoto typu. Stanovené výsledky jsou porovnány s výsledky experimentálního modelování. V práci je také otestována citlivost modelů na změnu velikosti prvku a počet prvků po tloušťce., Modal analysis of printed circuit board results, gained from computional and experimental modeling, have been compared. Anylyses have been performed on dummy boards (models without electronic components), created as one-layered at first, then as three-layered PCB. Board is usually clamped by its longer edges with wedgelock. In order to enable the realization of boundary conditions in computional and experimental modeling, real clamping has been simplified to simply supported. Computional models have used FEM elements, which are comomnly used in this type of problem. Determined results have been evaluated by comparing the experimental modeling results. Models‘ sensitivity on modification of element length and number of elements through thickness have been performed.