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A large-span steel–concrete composite beam with precast hollow core slabs (CBHCSs) is a relatively new floor structure that can be applied to various long-span structures. However, human-induced vibrations may present serviceability issues in such structures. To alleviate vibrations, both the walking forces excited by humans and the associated floor responses must be elucidated. In this study, 150 load–time histories of walking, excited by 25 test participants, are obtained using a force measuring plate. The dynamic loading factors and phase angles in the Fourier series functions for one-step walking are determined. Subsequently, walking tests are performed on seven CBHCS specimens to capture the essential dynamic properties of mode shapes, natural frequencies, damping ratios, and acceleration time histories. The CBHCS floor system generally exhibits a high frequency (> 10 Hz) and low damping (damping ratio

In this paper, free and forced vibration analysis of stiffened plates are investigated with the help of ANSYS Parametric Design Language (APDL) the codes were focused on the theory of First-order Shear Deformation Theory (FSDT). The CAD models were designed in Creo Parametric 6.0 with different cross-sections of stiffener and different boundary conditions were applied on the plate. For free vibration on stiffened plates modal analysis is carried out to identify natural frequencies and different mode shapes. Harmonic analysis has done under the application of pressure 150 kPa on the plate with the help of the mode superposition method further comparing the deflection at resonance frequencies of the plate with different cross-section and boundary conditions. Stiffened plates are extensively used in structural elements in civil engineering, marine constructions, aerospace application, railways, and industrial applications.

From recent years damage detection in composite structures is given a prior attention to avoid failure and breakdown of the structures. Delamination in composite structures is one of the main reasons for the failure and also affects the properties of the composite structures. Carbon fibre reinforced composite has a wide applications in industries which requires monitoring and detection of delamination for proper functioning. There are various methods such as non-destructive methods, mathematical models etc. to detect the delamination but are quiet costly, time taking and inefficient. In the present investigation, Artificial neural network (ANN) is used to determine delamination defect in carbon fiber reinforced polymer composite. ANN model can solve complex problems. Hence, the ANN model is developed to predict the delamination length and location from the fixed end by analyzing the first three carbon fiber composite structures three natural frequencies. The natural frequencies and mode shapes are obtained using finite element analysis (FEA). It has been found that the ANN can predict delamination length and location in carbon fiber reinforced polymer composite.

This paper has been devoted to exact calculation of the natural frequencies for out-of-plane free vibration of three-layer symmetric sandwich beams by using dynamic stiffness matrix method. Governing differential equations of motion have been derived using Euler-Bernoulli beam theory and St. Venant’s torsion theory, so that the effects of shear deformation in the face layers and rotary inertia are not taken into account and the cross-section is allowed to warp without restraint. Wittrick-Williams algorithm has been used to calculate the natural frequencies. Accuracy and ability of the dynamic stiffness matrix method have been illustrated in form of several examples. Results are verified through comparison with the natural frequencies obtained from ABAQUS software. Full independence of out-of-plane bending and torsional modes of vibration for three-layer symmetric sandwich beams has been proven.

This study investigates the behavior of simple and continuous span steel box girder bridges after various damage scenarios, including bracing failure and girder fracture, and develops a non-contact bridge health monitoring technique based on the bridge dynamic responses. A series of field tests were conducted to study the feasibility of using non-contact sensors to capture the bridge dynamic responses. Moreover, detailed finite element models of the bridges were developed and validated using the field test and available experimental test results and were used to investigate the bridge failure mechanisms, maximum load-carrying capacity, alternative load paths, and dynamic responses. The bridge dynamic analysis after damage showed that bridge frequencies are sufficiently sensitive for identifying partial or full-depth girder fracture in the simple span bridges. However, these significant damages may cause very small changes in the natural frequencies of continuous span bridges. The results show a significant change in the mode shapes after damage in both simple and continuous span bridges. The mode shapes are sensitive enough to detect damage at the inflicted locations, in most cases with better resolution when compared to the frequency changes. The comparison of the intact and damaged bridge mode shapes indicates that damage at different locations along the bridge has different amplitude changes in the mode shape that could be used to localize the damage. Moreover, the analyses show that either the individual modal sensitivities or combined sensitivities are indicative for most locations throughout the span. The results also indicate a clear pattern of changes in the frequency and mode shape for each damage scenario that can be used to detect the damage type, severity, and location along the bridge.

In this paper, finite element model (FEM) updating of masonry minarets was conducted by using dynamic characteristics obtained from Operational Modal Analysis (OMA). For numerical application, Mustafa Sahin mosque minaret in Turkey’s Elazig province was selected. In the finite element modelling, structure-foundation-soil interaction was considered. Soil, foundation and structure domains were assumed to be linearly elastic. The masses of foundation and soil were ignored. The FEM updating was performed by comparing the frequencies and mode shapes obtained from the FEM solutions with those of the experimental (OMA) method. The compatibility of numerical and experimental modes was controlled by the Modal Assurance Criterion (MAC) values. The FEM solutions were obtained by using ANSYS finite element package program.

This paper presents damage identification and localization in laminated composite beams including multiple cracks by automated model updating. For this aim, a cantilever beam made of glass/epoxy composite laminate under six simulated damage scenarios is considered. Experimental frequencies and mode shapes of the beam are validated with those of ANSYS® finite element analyses. For damage detection and localization, FEMtools®, a software for automated model updating, is employed. To simulate damages in FEMtools®, material moduli and mass density of the beam are chosen to be uncertain parameters, and the sensitivity analysis based on the Bayesian parameter estimation is performed. In-plane material moduli are found to be the most sensitive parameters for damage evaluation in composite laminates. The locations of the cracks are determined by evaluating the changes (decrease) in these parameters. According to the results of the study, the proposed method can locate the multiple cracks of different severity for the considered cantilever beam. However, in the case with multiple damages of equal severity, only the crack nearest to the fixed-end can be successfully determined while others cannot because the existence of damage near the support in cantilever beams obscures the effects of other damages and the method fails to identify them.

Progressive updating strategies are commonly used for the calibration of numerical models such as those of a track-bridge system. These strategies involve, first, updating the track model based on dedicated dynamic tests, and second, the calibration of the bridge model based on ambient vibration tests considering the updated track parameters. This subsequent procedure is suggested as some track parameters are, in relation to the modal responses of the bridge, generally not sufficiently sensitive for a successful parameter estimation. This work describes the calibration of a specific finite element (FE) model of a track section over a bowstring-arch railway bridge. The model includes the rails, rail pads, sleepers, the ballast layer and the interfaces with the bridge and neighbouring track sections. A track receptance test allowed for the identification of natural frequencies and mode shapes of the track by applying two different techniques, an output-only and an input-output. Several modes of vibration related to the movement of the sleepers on the ballast were identified using the SSI-DATA method, at frequencies between 83.8 Hz and 142.2 Hz. The calibration of the track FE model was performed using an iterative methodology by means of a genetic algorithm, which proves efficiency and robustness in estimating several track numerical parameters, besides a significant upgrade in relation to the numerical model before calibration.

The definition of the spatial variability of the ground motion (SVGM) is a complex and multi-parametric problem. Its effect on the seismic response of cable-stayed bridges is important, yet not entirely understood to date. This work examines the effect of the SVGM on the seismic response of cable-stayed bridges by means of the time delay of the ground motion at different supports and of the loss of coherency of the seismic waves. The focus herein is the effect of the SVGM on cable-stayed bridges with various configurations in terms of their length and of design parameters such a s t he pylon shape and the pylon–cable system configuration, combined with the influence of the incidence angle of the earthquakes. The aim of this paper is to provide general conclusions that are applicable to a wide range of cable-stayed bridges, instead of attempting to interpret the effect SVGM on a case-by-case basis, and to contribute to the ongoing effort to interpret and predict the effect of the SVGM. It has been found that the effect of the SVGM on the seismic response of cable-stayed bridges varies depending on the pylon shape, height and section dimensions, on the cable-system configuration and on the response quantity of interest. Furthermore, the earthquake incidence angle defines whether t he S VGM is important t o t he seismic response of the cable-stayed bridges. It is also observed that the SVGM excites vibration modes of the bridges that do not contribute to their seismic response when identical support motion is considered.

Trusses are everywhere; they are used in bridges, antenna towers, cranes, even in parts of the International Space Station. And for good reason, they allow us to create strong structures while using materials in very efficient and cost-effective way. Trusses it is essentially a rigid structure made up of a collection of straight members. The type of truss depends on how the horizontal and diagonal beams are arranged.

Dynamic analyses are necessary problems in offshore jacket structures design and assessment. These analyses have various applications in recognition of dynamic behavior, fatigue analysis, damage detection, etc. Natural frequencies and mode shapes, as inherent vibrational features of a structure, are key parameters in referred analyses. These parameters are mainly affected by mass and stiffness matrices and slightly by damping. Therefore, it is more important to estimate the stiffness matrix of a structure accurately, especially in stiff structures such as offshore jacket platforms. In many cases, the stiffness of levels is required. For example, it can be useful in the construction of an equivalent shear building model. This reduced equivalent model can be useful in damage detection, soft-story control in design criteria, or a simple vibrational model in frequency domain analyses. So, using a simple, fast and reliable method to general and primary calculation of stiffness of such a structure can be efficient. This paper deals with the assessment of six different stiffness calculation methods and implementation of them on a service offshore jacket structure installed in the Persian Gulf. The main idea in the definition of methods is the difference in load pattern and boundary conditions. Level lateral and torsional stiffness of the structure is calculated using the methods and compared with values extracted by the Finite Element Method (FEM). In addition, sensitivity analysis of methods carries out for such a platform. The results show that the right recreation of lateral modal specifications, unlike torsional mode, are very sensitive to the equivalent stiffness calculation method. In addition, it is shown that methods based on wave or earthquake load patterns are the best solution to reach the right model.

The dual wall-frame structure consists of a structural wall system and a rigid frame system, and there is a strong interaction between the frame and wall systems in the top and bottom of structures. Therefore, the structural response of the dual wall-frame structures is entirely different from that of the single structural system. This paper presented a modification on the modal-based ground motion selection (MGMS) procedure for concerning the distinct structural behaviour of wall-frame structures to properly consider the effect of frequency contents combination in the time domain (FCCTD) of input ground motion (IGMs) in selecting IGMs for the nonlinear response time history analysis (NLRHA) of the structure. The MGMS procedure for wall-frame structures (MGMS-WF) employed a pseudo-first mode with a uniformly distributed mode shape and selected IGMs that induced the most significant interaction of the first three modes or the pseudo-first, second and third modes from a suite of seed IGMs for the NLRHA of wall-frame structures. A comprehensive case study was conducted involving four reinforced concrete (RC) wall-frame structures with different heights and combinations of wall and frame. To verify the capability of the MGMS-WF in consistently selecting proper IGMs for the NLRHA of wall-frame structures, design spectra and conditional mean spectra with various construction conditions were employed as target spectra to select and scale seed IGMs. The results show that the seismic demands of wall-frame structures computed using the MGMS-WF-IGMs have high yet consistent reliability.

Abstrac Chatter is the main limiting factor affecting the material removal rates of machine tools and is caused by the machine's most flexible structural mode shapes. The use of active vibration control systems can damp the structural mode shapes and, in turn, significantly increase the chatter-free depth of cut. In order to reduce the commissioning effort, previous publications have introduced methodologies to automatically tune various control strategies for active damping. This paper presents a new automatic tuning approach for a robust model-based controller, which uses particle swarm optimization to find the best-performing control parameters. The proposed method was tested on both a 5-axis milling machine and a vertical lathe, together with an automatically tuned direct velocity feedback controller and an adaptive controller. The performance was evaluated by conducting extensive cutting tests under industrial operating conditions. All controllers and automatic tuning methodologies led to notable increase in chatter-free material removal rates, reduced vibration amplitudes, and improved surface roughness.

This report analyzes the reproducibility of the article “Computing Planetary Interior Normal Modes with A Highly Parallel Polynomial Filtering Eigensolver” by Jia Shi et al. (Shi, 2018). To reproduce the results we perform different weak and strong scaling studies using a series of Mars models. All experimental runs were performed during the SC19 Student Cluster Competition on a four node Intel Skylake cluster. We show that the findings of the original article can be reproduced in a different environment.

The article aims to assess possibilities of using probabilistic methods for calculating seismic resistan of buildings based on the laws of structural mechanics. The design schemes and models of buildings rigidly embedded in the base and with a seismic isolation device are described. Formulas developed on the basis of the law of energy conservation, namely the seismodynamic law, which allow to estimate the coefficient of dynamism, are presented. It is proposed to abandon the main modes of vibration in the calculations, i.e. the coefficient ηir of the waveform and the vibration frequency of the residential building and the foundation during earthquakes. Shear and bending calculations of a residential building are based on the design model developed. The values of seismic force are determined by the first and last modes of vibration. Based on these values, it is proposed to calculate internal forces and deformations in the bearing structures of buildings using the methods of structural mechanics.

Wind turbines are becoming larger to produce more power from the wind in a given area. While the large-size wind turbines are advantageous in terms of generating power, the blades are very heavy and difficult to transport and install. General Electric Co. and the National Renewable Energy Laboratory proposed a new blade design and manufacturing concept that covers the blade with tensioned fabrics. This fabric-covered wind turbine blade is composed of spar-rib structures and covering fabric skins. The present study investigates the aerodynamic effects of fabric skin. A fluid–structure interaction (FSI) analysis was performed about the fabric skin of a large-sized fabric-covered blade. Through static and dynamic FSI analyses, the response of the fabric skin was analyzed according to the wind speeds. The natural frequencies and mode shapes were compared. It was confirmed that the tension of the fabric skin should be increased as much as possible to maintain aerodynamic efficiency, and in addition that the natural frequencies and mode shapes were changed by the wind speeds.

To consider the influence of the quality of the accelerometer and the installation position on the test frequency, a test scheme was designed to identify the first-order bending frequency with free and cantilever beams as well as the first-order torsion frequency with free plates. According to the energy method and mode shape, the correction relationship between the elastic modulus and the first-order bending frequency of free and cantilever beams is derived alongside the relationship between the shear modulus and first-order torsion frequency of a free plate. These relationships are suitable for informing the influence of the accelerometer mass and installation. The first-order bending frequency and the first-order torsion frequency of Sitka spruce beams, slabs, and oriented strand board have been measured along the length, which verifies the effectiveness of the derived relation in testing the elastic modulus and shear modulus of wood materials. Taking the ratio m/M between the mass of the accelerometer and the mass of the test specimen as a parameter, the scope of application of the modified relation is discussed.

Ever-increasing scarcity of land and demand for high-rise structures has significantly contributed to the use of combined piled raft foundations (CPRF) in soft ground. However, utility, design constraints and aesthetic considerations bring asymmetry to superstructures, making structures more vulnerable during seismic excitations. Traditional design practices involve designing superstructure elements and foundation considering fixity at the base of the superstructure and ignoring soil-structure interaction (SSI) which may result in under-estimation of forces and displacement in the system. Hence, the present study aims at developing new seismic design guideline pertaining to asymmetric single and multi-storied structure supported on CPRF embedded in soft clay. Some important parameters, such as torsional coupling mode of vibration and multi-storey idealisation involving the effect of higher modes are investigated incorporating seismic SSI effect. The study broadly reveals that the torsional to lateral period ratio considerably influence the seismic response of asymmetric structural system on the piled raft foundation due to the incorporation of SSI. Furthermore, multi-storey building idealisation gives a higher estimation of response compared to single storey idealization in superstructure and pile head which may be due to the effect of higher modes of vibration and SSI

A manufacturing study of a 0.372 THz 8-fold (8F) helically corrugated interaction region (HCIR) and measurement of its wave dispersion characteristics are reported. This demonstrates the structure’s suitability as the electron beam / electromagnetic wave interaction region in a high power frequency tunable Gyroresonant THz source. The 8F HCIR has an eigenmode, which is ideal for broadband tuning, created by the coupling of the TE61 and TE23 modes. Maximum power handling of 14 times larger than a 3-fold HCIR at the same frequency is calculated. A TE11 to TE61 7-fold (7F) helically corrugated waveguide (HCW) mode converter, needed to measure the wave dispersion of the 8F HCIR, was designed and constructed. Negative aluminium mandrels of the 7F HCW mode converter and 8F HCIR were manufactured. Copper structures were constructed through electroforming. The measured wave dispersion of the 0.372 THz 8F HCIR agreed well with simulated dispersion characteristics.

This paper deals with the modal analysis of optimized trapezoidal stiffened plates with simple supported conditions on the four edges of the base plate. The main objective of the finite element analysis is to investigate the natural frequencies and mode shapes of some stiffened structures subjected to lateral pressure and uniaxial compression in order to identify any potentially dangerous frequencies and eliminate the failure possibilities. The natural frequencies and mode shapes are important parameters in the design of stiffened plates for dynamic loading conditions. In this study, the numerical analysis is performed for such a design of this kind of welded plates which have already been optimized for lateral pressure and uniaxial compression. The objective function of the optimization to be minimized performed with the Excel Solver program is the cost function which contains material and fabrication costs for Gas Metal Arc Welding (GMAW) welding technology. In this study, the eigenvalue extraction used to calculate the natural frequencies and mode shapes is based on the Lanczos iteration methods using the Abaqus software. The structure is made of two grades of steel, which are described with different yield stress while all other material properties of the steels in the isotropic elastic model remain the same. Drawing the conclusion from finite element analysis, this circumstance greatly affects the result.

In this study, we use a large-scale parameter analysis and linear regression method to characterize the static stability of Kiewitt-sunflower-type single-layer reticulated spherical shell. Based on more than 15,000 numerical cases of elastic–plastic load–displacement process, and the investigations on the influence of buckling and instability mode, rise-span and ring-numbers ratio, efficiency of the structure, load distribution, support conditions, size of the initial geometric imperfection and distribution patterns are proceeded. We summarize the key effect for stable performance of structure, and develop the formulation to calculate the ultimate capacity of stability. The results show that Kiewitt-sunflower type single-layer reticulated spherical shell is sensitive to defect, and different distribution patterns of geometry defect lead to different structural buckling. The ultimate stability bearing capacity can be improved by increasing the rise-span and ring-numbers ratio. The asymmetrical load distribution has little effect on the stability. The most unfavorable eigenmode is arbitrary, and it is generally not the lowest order. We summarize the key effect for stable performance of structure, and develop the formulation to calculate the ultimate capacity of stability.

The natural frequencies corresponding to the particular mode shapes of a large turbo-generator must not be in the resonance region before delivery. Different parameters may clearly affect these dynamic characteristics. Different from other studies, this paper introduces a method for obtaining the inherent characteristics of end winding in a short period of time under multiple simultaneously changing parameters. The proposed process is based on the response surface method (RSM). In this method, the main concerned natural frequencies were taken as the critical index to describe the dynamic behaviors of the end winding, with which the mathematical relationship between the dynamic characteristics and design variables was analyzed. First, the stiffness of the rings, stiffness of the radial braces and number of pins bonded to the radial braces were used as samples for orthogonal experimental design. Then, the natural modes and frequencies of 25 different samples were acquired by conducting modal analysis with ABAQUS software. Utilizing these dynamic results, a second-order polynomial response surface model was established to describe the relationships between natural frequencies and these three different parameters. Then, the quality of this model was verified by calculating the valuating indexes for comparison with support vector regression (SVR). With the response surface model, the variation regularities of the natural frequencies and modes due to the above parameters were discussed. The method proposed in this paper can enable natural frequencies in the whole design space to be quickly determined without finite-element analysis, greatly improving the development efficiency and laying a foundation for dynamic response prediction during normal operation with different parameters and additional large turbo-generator stator end winding optimization.

In this paper, an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material (FGM) using stationary wavelet transform (SWT) and neural network (NN). Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution. Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth. The dynamic stiffness method (DSM) is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams. The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification. The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures, even with noisy measured mode shapes and a limited amount of measured data.

The electric solar wind sail (E-sail) has been proposed as a novel propulsion system that, if successful, promises to facilitate missions that would be inconvenient or impractical with traditional chemical propellants. The most common E-sail concept includes a central hub with several long positively charged tethers extending radially outward that harvest momentum from protons in the solar wind. Before the technology is ready for a demonstration mission, we must prove E-sail dynamics can be controlled throughout all phases of the mission. The objective of this paper is to present an analytical model for the linear vibrations of hub and spoke E-sails to facilitate the development of necessary control schemes. Although there is no limit to the number of spokes in our model, we demonstrate its capability by representing a system with 3 spokes. The resultant natural frequencies and mode shapes provide insight into the dynamics and stability of E-sails and lay the foundation for development of control schemes. In addition, our work reveals several simple calculations that accurately estimate many of the natural frequencies and could be used to facilitate the design of future E-sails.

This study attempts to propose an internal vibration isolation technology applied to the marine gearbox by exploring the impact of vibration isolators on the vibration response of gearbox case. The spring element COMBIN14 of ANSYS software is used to simulate the vibration isolators installed between the inner and outer shells of the marine double-layer gearbox case. The modal of the marine double-layer gearbox case is calculated by the Lanczos method. The structural vibration responses of two gearbox cases are calculated by the modal superposition method. The effect of the vibration isolator on the gearbox case is evaluated by the vibration acceleration and acceleration-vibration level difference. The first six modal vibration modes of the double-layer gearbox case are inner shell vibration. The vibration acceleration of the double-layer gearbox case on the outer shell is less than that of the single-layer gearbox case. The vibration acceleration is positively correlated with the vibration-isolator number on the outer shell. The vibration reduction performance of the double-layer gearbox case decreases with the increase of the vibration-isolator stiffness when the stiffness is in the range of 1.0 × 107–1.5 × 109 N/m. The acceleration-vibration level of the double-layer gearbox case is negatively associated with the number and stiffness of vibration isolators. The vibration isolator plays an important role in the vibration reduction of the marine gearbox. The performance of the vibration isolator would be weakened as the number and stiffness of vibration isolators increase.

It is well known that the vertical vibrations of lightweight timber floors would cause discomfort to the occupants. As a new kind of flooring system, the metal-plate-connected timber truss joist floors were developed due to their larger spans and easier crossing of pipes and cables after sawn timber and I-joist floors. In this paper, the vibration modes and transfer functions of sixteen metal-plate-connected timber truss joist floors over a nominal span of 6 m were determined experimentally to measure the changes in vibration frequencies and transmissions obtained after the installation of strongbacks and strappings. The results showed that the fundamental natural frequencies of the metal-plate-connected timber truss joist floors at a 400 mm joist spacing were about 15 Hz, while the frequencies of the floors at a 600 mm joist spacing were about 12.5 Hz. The bracing elements of the strongbacks and strappings mainly enhanced the system stiffness in the across-joist direction of the flooring system, but they did not govern the fundamental natural frequencies of the floors and just changed the spacing of adjacent natural frequencies. The bracing elements as secondary elements of the floors also altered the vibration transmission paths in the across-joist direction. The frequencies where the stronger vibration transfers happened in the direction perpendicular to floor joists were generally above 15 Hz. Proper installation measurements of bracing elements in practical control need to be taken to alleviate the vibration response intensity at the targeted locations and frequencies.

A simple method of calculation of lateral critical speeds of flexible rotors with rigid supports is presents is presented. The method is mainly based on the former work of Myklestad and Prohl and considers the shaft to be divided into a number of finite elements connected by massless elastic sections. A digital computer program is then prepared to solve the finite equations resulting from the analysis. By means of this program, the critical speeds of flexible rotors can be predicted at different stiffnesses of the rigid supports and mode shape of the whirling rotor is predicted. An actual cases of a centrifugal compressor rotor having different characteristics is considered.

Earthquakes have the highest rate of mortality among the natural disasters and regularly lead to collapsed structures with people trapped inside them. When a reinforced concrete building collapses due to an earthquake, many of the concrete elements (i.e., beams and columns) are damaged and there are large sections where the concrete is missing and the steel reinforcement is exposed (i.e., concrete discontinuities). The prediction of vibration transmission in collapsed and severely damaged reinforced-concrete buildings could help decisions when trying to detect trapped survivors, hence there is need for experimentally validated finite element models of damaged concrete elements. This paper investigates the dynamic behaviour of damaged reinforced concrete beams using Experimental Modal Analysis (EMA) and Finite Element Methods (FEM). FEM models are assessed using two beams with one or more concrete discontinuities that form dowel-type joints. These models used either beam or spring elements for the exposed steel bars and were experimentally validated against EMA in terms of eigenfrequencies and mode shapes. Improved agreement was achieved when using springs instead of beam elements in the FEM model. The comparison of mode shapes used the Partial Modal Vector Ratio (PMVR) as a supplement to the Modal Assurance Criterion (MAC) to confirm that spring elements provide a more accurate representation of the response on all concrete parts of the beams.

Purpose This study aims to include the diagnosis of an old concrete deck steel truss rural road bridge in the damaged and retrofitted state through vibration response signals. Design/methodology/approach The analysis of the vibration response signals is performed in time and time-frequency domains using statistical features-root mean square, impulse factor, crest factor, kurtosis, peak2peak and Stockwell transform. The proposed methodology uses the Hilbert transform in combination with spectral kurtosis and bandpass filtering technique for obtaining robust outcomes of modal frequencies. Findings The absence or low amplitude of considered mode shape frequencies is observed both before and after retrofitting of bridge indicates the deficient nodes. The kurtosis feature among all statistical approaches is able to reflect significant variation in the amplitude of different nodes of the bridge. The Stockwell transform showed better resolution of present modal frequencies but due to the yield of additional frequency peaks in the vicinity of the first three analytical modal frequencies no decisive conclusions are achieved. The methodology shows promising outcomes in eliminating noise and visualizing distinct modal frequencies of a steel truss bridge. Social implications The findings of the present study help in analyzing noisy vibration signals obtained from various structures (civil or mechanical) and determine vulnerable locations of the structure using mode shape frequencies. Originality/value The literature review gave an insight into few experimental investigations related to the combined application of Hilbert transform with spectral kurtosis and bandpass filtering technique in determining mode frequencies of a steel truss bridge.

We have developed a general method, dubbed the split beam method, to solve Euler–Bernoulli equations for cantilever beams under multiple loading conditions. This kind of problem is, in general, a difficult inhomogeneous eigenvalue problem. The new idea is to split the original beam into two (or more) effective beams, each of which corresponds to one specific load and bears its own Young’s modulus. The mode shape of the original beam can be obtained by linearly superposing those of the effective beams. We apply the split beam method to simulating mechanical responses of an atomic force microscope probe in the “dynamical” operation mode, under which there are a stabilizing force at the positioner and a point-contact force at the tip. Compared with traditional analytical or numerical methods, the split beam method uses only a few number of basis functions from each effective beam, so a very fast convergence rate is observed in solving both the resonance frequencies and the mode shapes at the same time. Moreover, by examining the superposition coefficients, the split beam method provides a physical insight into the relative contribution of an individual load on the beam.

Design structures to resist natural hazards is a vital issue to mitigate the impact of such threats. Earthquakes could lead to numerous injuries and infrastructure destruction. Specifically, when structures are not designed to resist seismic load. This article presents dynamic analysis of four-story shear frame under moderate ground motion to determine the dynamic response. The proposed location of the considered frame is near Iraq-Iran border due to increase of seismic activities in last years. Structures in the considered seismic zone are essentially either residential or commercial buildings and not designed to resist seismic load, therefore structural system failure is probable. Simplified model is considered to determine response spectrum according to the International Building Code requirements. The algorithm of the analysis is developed using MATLAB® code to get mode shapes, response spectrum acceleration, maximum displacement, maximum shear forces, and modal participation mass at each story. The article develops design response spectra curve of Erbil city. Furthermore, the analysis results showed that first mode shape has more contribution than the other modes because higher percentage of the mass of the shear frame responds to the ground motion, and 88.53% of shear-frame mass is participating responds to the ground motion in the same mode. Conclusions The current study computed dynamic response spectrum of multi-story shear frame located in northern of Iraq near borders with Iran due to significant activities in last years. While the topic is well known in the structural dynamics filed, but the application of the current study is ever pressing since most of structures have not been designed to resist earthquakes and casualties and losses is probable. Numerical evaluation has been performed of four-story shear frame subjected to ground motion using MATLAB®. The design response spectrum is predicted for Erbil city which is located north of Iraq since moderate-scale earthquakes have been noticed in last years. Design structures to resist seismic load is essential to protect occupants and reduce losses. The framework of the study consists of running modal analysis to calculate the natural frequency, period and mode shapes of the shear-frame. The response spectrum matrix is calculated according to IBC code requirements. Furthermore, peak modal displacement, total shear at each story level are determined using square root of the sum of the squares (SRSS) combination method. Finally, the results of the analysis showed 88.53% of shear-frame mass is participating responds to ground motion in the first mode.

This article deals with the investigation of delamination effects on the flutter behavior of a composite wing subjected to unsteady aerodynamic loads by providing an integrated procedure using exact methods. For this purpose, an undamaged wing structure is modeled as a cantilevered Bernoulli–Euler beam with coupled bending–torsion and delaminated wing structure is modeled as three interconnected intact beams. The modal analysis of the intact and delaminated beams is performed and mode shapes are obtained based on the development of the dynamic stiffness matrix, a computer code and an iterative method. The fundamental modes of the intact and delaminated beam derived from the free vibration analysis are used in Galerkin’s method and the flutter and divergence speeds are obtained with aerodynamic forces applied. In fact, modified shape functions were developed to reflect the delamination effect in the aeroelastic analysis. Also, for the unsteady aeroelastic analysis, an iterative algorithm is developed. It was found that the delamination location and its length can have a positive or a negative influence on the flutter behavior of the wing which depends on the fiber angle.

The spatiotemporal origin of plasmonic chiroptical responses in nanostructures remains unexplored and unclear. Here, two orthogonally oriented Au nanorods as a prototype were investigated, with a giant chiroptical response caused by antisymmetric and symmetric mode excitations for obliquely incident left-handed circular polarization (LCP) and right-handed circular polarization (RCP) light. Time-resolved photoemission electron microscopy (PEEM) was employed to measure the near-field spatial distributions, spectra, and spatiotemporal dynamics of plasmonic modes associated with the chiroptical responses at the nanofemto scale, verifying the characteristic near-field distributions at the resonant wavelengths of the two modes and a very large spectral dichroism for LCP and RCP. More importantly, eigenmode excitations and their contributions to the ultrafast plasmonic chiroptical response in the space-time domain were directly revealed, promoting a full understanding of the ultrafast chiral origin in complex nanostructures. These findings open a way to design chiroptical nanophotonic devices for spatiotemporal control of chiral light-matter interactions.

Among vibration-based damage detection methods, one of the effective approaches for damage localization is the modal strain energy method. In this paper, the modal strain energy method is developed for damage detection in plate-like structures with various boundary conditions. Firstly, the theory of the modal strain energy method is briefly outlined. In order to overcome the limitation of measuring points, a central difference method is newly employed to compute the partial differential terms in the modal strain energy formula. Finite element analysis is conducted on an aluminum thin plate to obtain the mode shapes before and after the occurrence of damage. Feasibility of the proposed method is verified by investigating plates with different types of boundary conditions. A damage index is presented to identify the location and extent of crack in the plate-like structures. The analytical results show that the proposed method accurately identifies the crack in the plate structure with various types of boundary conditions by using appropriate mode shapes and damage threshold.

An improved finite element modeling method is developed for isotropic curvilinearly stiffened plates under a thermal environment. The existing modeling method for curvilinearly stiffened plates avoids the difficulty of node overlap, which is suitable for plates with different thicknesses. By introducing the influence of temperature on material parameters and thermal stress on additional stiffness, the existing method is improved and extended to the study of thermodynamics. The proposed method is verified by modal test at normal temperature and commercial finite element software at the thermal environment. The variation of dynamic characteristics with temperature under different boundary conditions was studied. Results show that when the boundary conditions are asymmetric, the influence of temperature on the thermal mode shape is more significant than the case of symmetrical.

Slamming against the wet deck of a multihull vessel in head sea waves is studied analytically and numerically. The theoretical slamming model is a two-dimensional, asymptotic method valid for small local angles between the undisturbed water surface and the wet deck in the impact region. The disturbance of the water surface as well as the local hydroelastic effects in the slamming area are accounted for. The elastic deflections of the wet deck are expressed in terms of "dry" normal modes. The structural formu­lation accounts for the shear deformations and the rotatory inertia effects in the wet deck. The findings show that the slamming loads on the wet deck and the resulting elastic stresses in the wet deck are strongly influenced by the elasticity of the wet deck structure.

The high and slender historical masonry minarets are vulnerable to the static and dynamic loads. Performance analyses of minarets are implemented using three-dimensional numerical models in recent years. However, the complex and inhomogeneous nature of historical structures increases the likelihood of incorrect creation of numerical models. For that reason, it is important to know the experimental dynamic characteristics of masonry minarets to update the numerical models accordingly. However, it is very difficult and costly to conduct in-situ tests for every minaret. The present paper aims to develop a simplified fundamental frequency formula based on in-situ ambient vibration tests for historical masonry stone cylindrical minarets. Nineteen historical masonry stone cylindrical minarets are chosen for this purpose. Firstly, experimental frequencies, mode shapes and damping ratios of the selected minarets are determined and evaluated using the experimental measurements. Enhanced Frequency Domain Decomposition (EFDD) technique is used to obtain the experimental dynamic characteristics. Based on the obtained experimental natural frequencies, the correlation of the first natural frequency with various geometrical parameters of minaret is demonstrated by the regression analyses. In order to verify numerical models of the masonry stone cylindrical minarets, a simplified fundamental natural frequency formula based on the minaret geometrical dimensions is proposed using the experimental natural frequencies. In addition, coefficients for estimating the second and third frequencies are also presented. It has been observed that the proposed formula gives very consistent results with the measurement and literature data.

The separation of cross section’ mass center from its centroid will lead to coupled bending and torsional vibration of the wind turbine tower (Referred to as tower). Three governing differential equations of vibration of the tower with inhomogeneous material and variable cross section are formulated based on D'Alembert's principle and Euler-Bernoulli beam theory. Considering the installation and operation factors of the wind turbine, the dimensionless natural frequencies and mode shapes of the tower under multiple constraint conditions are obtained by the differential quadrature method. Compared with those available in the literature, numerical results demonstrate the accuracy and validity of the proposed method. A series of parametric study is accomplished to reveal the influence of the foundation stiffness, wall thickness, eccentricity, and the ratio of the inner diameter of the top and bottom cross section of tower on the vibration characteristics of tower. The frequencies veering for the mode of tower is discussed. These numerical results have guiding significance for the design of tower.

Two excitation methods based on 2D normal mode were proposed using two piezoelectric transducers (PZTs) with opposite phase and in-phase to excite the two dimensional normal modes of (1, 1) and (2, 1), respectively. The theoretical models of the excitation modes were deduced by the wave equation. An ultrasonic separator was built and the acoustic simulation of the ultrasonic excitation modes was modeled in Ansys software. The simulation results of the sound pressure distribution in the flow channel show that (1, 1) and (2, 1) are successfully excited. The micro-separator with 8 mm width and 0.2 mm high flow channel was fabricated on silicon on insulator (SOI) by micro-processing technology to form a perfect reflection layer of the separator. An experimental platform was established and the results show that both excitation methods can achieve the separation of suspended particles with high-through of 100 μL/min. In the experiment of (1, 1) excitation method, it can be seen that most of the particles converge in the center of the separation cavity into a large bunch, and in the experiment of (2, 1) excitation method, the particles mainly converge on both sides of the separation chamber. Both methods can successfully separate suspended particles out of the fluid.

We search in the continuous GPS 3-D displacement data for the signals of the normal modes of Earth’s free oscillation that were excited by the 2011 Mw 9.0 Tohoku earthquake. A previous study has reported such a detection; we here conduct a more comprehensive and detailed study. We use GPS data from three separate networks: (i) about 1000 stations from the Japan GEONET; (ii) about 600 stations from the western USA PBO; and (iii) about 140 stations of the global IGS, and solve and form records of 21 h length at 30-s sampling rate. We conduct various multiple-record stacking methods: the frequency-domain power spectrum stacking that reduces the variance of the noises, and the time-domain stackings that boost the SNR of target modes while suppressing the non-target modes. We find the time-domain stacking method of optimal sequence estimation (OSE) to be the most effective, which show clearly high sensitivity and detectability of the modes in the spectrum. For the near-field GEONET where all excited modes have anti-nodes, all the spheroidal fundamental modes 0S9–0S43 below 5 MHz and some of the lower-degree overtones as well as most of the low-degree toroidal fundamental modes show up as prominent spectral peaks against the PREM model eigenfrequencies. The PBO sees less strong (being far-field and generally off-antinodes), but still clearly identifiable spectral peaks of the fundamental modes. The global IGS network data detect barely a handful of these modes because of its sparsity and small numbers of stations. We thus demonstrate that GPS does actually record the tiny seismic signals that can be revealed by means of multiple-record stacking methods, potentially useful for studying earthquake source mechanisms exciting the normal modes.

Dynamic analysis can be used to find dynamic displacements, time history, and the frequency content of the load. One analysis technique for calculating the linear response of structures to dynamic loading is a modal analysis. In modal analysis, we decompose the response of the structure into several vibration modes. A mode is defined by its frequency and shape. Structural engineers call the mode with the shortest frequency (the longest period) the fundamental mode. Holzer and Stodola's approximate methods for determining the forms and periods of oscillation for frame structures are presented in the paper. An approximation method, based on approximate relative stiffnesses of the storeys and the ground floor, is analyzed and proposed. The results obtained by the proposed approximate procedure do not greatly deviate from those obtained by more accurate calculations. It is therefore emphasized that the method can be used both in practice and for checking computer-based analysis of complex systems. At the end of the paper was given a comparison of the results obtained by approximate methods and some engineering software.

An ultrathin-film microring laser was fabricated using inkjet printing and a simple lift-off technique. Whispering-gallery-mode lasing was observed under optically pumped conditions in the film. The freestanding laser can be transferred to arbitrary surfaces for multifunctional applications, such as acoustic and relative humidity sensing. Using the first eigenmode of a membrane vibration, an acoustic sensor with a 0.15 Pa limit of detection was demonstrated via laser bandwidth broadening. A relative humidity sensor with a 1.1% limit of detection via wavelength shifts was demonstrated by placing the device on an optical fiber facet. These cost-effective, transferrable, multifunctional laser sensors will have many additional applications.

Base Isolation is a technology of mitigating the effects due to earthquakes with the aspect of dissipating the seismic waves away from the superstructure, by isolating the superstructure from the ground.This concept is widely essential to be implemented in structures(buildings) irrespective of many factors. There are several materials which could be implemented as base isolator, however the need in reduction of the number of the isolators is essential dueto various factors which a developing country finds difficult to implement. In this paper, a three-storey unsymmetrical building to be considered for the study is isolated by varying the mass of the foundation beam, (Transfer beam) thereby reducing the number of isolators in the building.Furthermore,the mode shapes and frequencies of the structure without base isolation and with base isolation considering mass of the base isolation system as a key factor were analysed and compared and hence the variation in the mass of the isolation system has a promising effect in altering the higher modes of vibration. The analysis is prolonged using another methd using UBC-1997 provisions and compared. In both the methods, the influence of the mass of the isolation system has a remarkable effect in altering the higher modes of vibration.

To reduce the errors caused by the rigid body hypothesis in the aerodynamics-structure coupling calculation and improve the structural performance, an optimum structure design with the consideration of the fluid-structure interaction are performed for the H-type vertical axis wind turbine (VAWT) blade. Based on the ANSYS Workbench platform, the geometric model, computational domain and grids of the wind wheel are constructed, the turbulence model, boundary conditions and composite material layers are set up, and the fluid and solid domains are solved in a coupled way. The single-objective structural optimization model in which the thicknesses of glass clothes, foam and gel coat, and the positions of two webs are taken as design variables is solved using the response surface optimization method to minimize the wind wheel mass. The frequencies and vibration modes of original and optimized blades with and without pre-stress and the transient characteristics of wind wheels in different wind speeds are investigated. The results indicate that after the blade optimization, the first-order frequency and critical speed become larger and other frequencies reduce for the static, single pre-stress and multiple pre-stresses states, and the maximum displacement, stress and strain of the wind wheel decrease under rated and extreme wind speeds, confirming significant performance improvements. The research provides useful guidance for the integrated design of structure and aerodynamics of wind turbine blades.

The concurrent evaluation of the vibration eigenfrequencies in densely polymer-tethered particle systems (“particle brushes”) by Brillouin light scattering and elastodynamic theory reveals a distinctive change of acoustic eigenmode formation associated with polymer graft modification of colloidal particles. The eigenfrequencies of particle brushes reveal a characteristic red-shift compared to uniform core-shell particles that can only be rationalized by assuming imperfect boundary conditions and anisotropic elastic properties of the graft layer. The distinct characteristics of vibration modes in particle brush materials provide direct evidence for the implications of chain confinement on the nanomechanical properties of tethered chains. The results highlight a rich and hitherto unexplored parameter-space for controlling properties and interactions in particle–brush based systems that could spur the development of hybrid materials with novel functionalities.

Structural damage caused by the vortex-induced vibration (VIV), harsh marine environment, and ultimate loads, etc., often alters marine risers’ natural frequencies and mode shapes. A simple method for calculating variable-tensioned marine risers, especially for the risers with single and multiple damages, is proposed herein to explore the relationships between modal characteristics and structural damage. The approach’ main advantage is that it is suitable for marine risers with various boundary conditions, variable tension, and different damage locations and degrees. Compared with the literature, the natural frequencies and mode shapes are re-examined using the intact marine risers. With the variation of damage degree and location along water depth, the effects of damage on natural frequency and the second derivative of mode curvature (SMC) are studied. To solve frequency and SMC’s insensitivity problem to the node damage, a frequency-square-weighted superposition of the SMC index, i.e., SSMC, is developed. The relationships of SSMC with the single damage and the multiple damages are accurately modeled, and the damaged severities are precisely predicted by fitting a cubic polynomial and a quintic-binary function, respectively. In total, the proposed methods and the numerical results may be useful references to the damage detection of marine risers.

Metamaterial with various degrees of bandgap tunability is an emerging area in manipulating elastic wave transmission characteristics for next generation phononic devices. Although several attempts are made employing multi-fields such as magnetic, electric and thermal etc., mechanical deformation based tunable bandgap is a major interest. However, achieving tunability in terms of broadening or terminating the bandgap in locally resonant acoustic metamaterial (LRAM) remains as challenging tasks. In this work, we propose LRAM by integrating a two-dimensionally periodically arranged square unit cells consisting of soft coated hard inclusion embedded in a polymer scaffold. We develop computational framework to simulate the low frequency bandgap of unit cell under external deformation. At first quasi-static analysis of unit cell has been performed to find static displacement field under prescribed deformation. Further, utilizing Bloch-Floquet wave analysis for the periodic unit cell and finite element based numerical scheme, an eigenvalue problem is formulated to predict dispersion response within irreducible Brillouin zone (IBZ). Analyzing the symmetry group of the unit cell under deformed state for a series of loading, we extract the bandgap responses. Moreover, we illustrate tunable bandgap at low frequency regimes for different inclusion shapes and sizes. To correlate extension and suppression of bandgap under the applied deformation, evolution of local resonances are described with vibration mode shapes.

Recently, space tethered satellite system has attracted widespread attention due to its attractive potential in space applications. Significant research on the tethered satellite formations has been undertaken to study the dynamics and control, vibration modes, tether models, and tether applications and it is generally assumed that the state information of the tethered satellite system is completely known or can be easily measured. However, few studies have been presented on the state estimates of the tethered formations. In this study, a state estimation scheme, with a minimal sensor fusion design, is presented for double-pyramid tethered satellite formations. The objective is achieved by fusing only the measurements of the two GPS sensors and the tether constraints. Furthermore, the observability of the proposed fusion design is proved through the analyses of Lie derivatives. Simulation results are presented that validate the proposed scheme. The proposed scheme provides a general hint of state estimation for a class of satellite formations with the tethered constraints.