• Smart Structures and Systems
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• v.13 no.5
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• pp.731-753
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• 2014

In this study, an indirect approach is developed for assessing the state of a bridge on the basis of mode shapes estimated by the responses of passing vehicles. Two types of damages, i.e., immobilization of a support and decrease in beam stiffness at the center, are evaluated with varying degrees of road roughness and measurement noise. The assessment theory's feasibility is verified through numerical simulations of interactive vibration between a two-dimensional beam and passing vehicles modeled simply as sprung mass. It is determined that the damage state can be recognized by the estimated mode shapes when the beam incurs severe damage, such as immobilization of rotational support, and the responses contain no noise. However, the developed theory has low robustness against noise. Therefore, numerous measurements are needed for damage identification when the measurement is contaminated with noise.

• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.531-550
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• 2008

This paper adopts the numerical assembly method (NAM) to determine the exact solutions of natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and springmass systems. First, the coefficient matrix for an intermediate station with various concentrated elements, cross-section change and/or pinned support and the ones for the left-end and right-end supports of a beam are derived. Next, the overall coefficient matrix for the entire beam is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact solutions for the natural frequencies of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and the associated mode shapes are obtained by substituting the corresponding values of integration constants into the associated eigenfunctions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.8 s.113
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• pp.886-892
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• 2006

Hot spot phenomenon is caused by non-uniform contact area between brake pad and disk frequent braking. Brake disk deformed by locally concentrated heat increases magnitude of frictional vibration. And this deformation can highly influence the judder vibration. In this experimental study, vibration and hot spot was measured in accordance with rotation of disk and pressure of master cylinder for finding the factors that causes hot spot phenomena. For comparing hot spot aspects with mode shapes of disk, mode shapes were measured by conducting modal test, and analyzed by using finite element analysis. Relation between hot spot phenomenon, and mode shape, pressure of master cylinder and rotation speed of disk respectively, was achieved by hot spot measurement and frequency analysis.

• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.229-245
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• 2012

Bridge vibration displacements have been directly measured by LVDTs (Linear Variable Differential Transformers) or laser equipment and have also been indirectly estimated by an algorithm of integrating measured acceleration. However, LVDT measurement cannot be applied for a bridge crossing over a river or channel and the laser technique cannot be applied when the weather condition is poor. Also, double integration of accelerations may cause serious numerical deviation if the initial condition or a regression process is not carefully controlled. This paper presents an algorithm of estimating bridge vibration displacements using vibration strains measured by FBG (Fiber Bragg Grating) sensors and theoretical mode shapes of a simply supported beam. Since theoretically defined mode shapes are applied, even high modes can be used regardless of the quality of the measured data. In the proposed algorithm, the number of theoretical modes is limited by the number of sensors used for a field test to prevent a mathematical rank deficiency from occurring in computing vibration displacements.89The proposed algorithm has been applied to various types of bridges and its efficacy has been verified. The closeness of the estimated vibration displacements to measured ones has been evaluated by computing the correlation coefficient and by comparing FRFs (Frequency Response Functions) and the maximum displacements.

• Structural Engineering and Mechanics
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• v.63 no.4
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• pp.551-565
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• 2017

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.840-840
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• 2003

Operational Modal Analysis (OMA) is a technique for identification of modal parameters by measurement of only the system's response. On many lightweight structures, such as load-speaker cones and disk drive read/write heads, is impossible or impractical to measure the input forces. Another characteristic of lightweight structure is their sensitivity to mass loading from sensors. The Scanning Laser Doppler Vibrometry(SLDV) allows response measurements to be taken without mass loading. One disadvantage of OMA testing compared to tradition input output modal testing is the OMA mode shapes are un-scaled. This means that the mode shape obtained from an OMA test can not used for analytical structural modification studies. However, the un-scaled mode shapes from an OMA test can be used to update a Finite Element Model (FEM). The updated FEM can then be used to analytically predict the effect of structural modifications. This paper will present the results of an OMA test performed on a simple plate and motor in operating conditions. The un-scaled mode shapes from this test will be used to update a FEM model of the system. The updated FEM model will be then be used to predict the effect of attaching a mass to the plate. The shapes predicted by the FEM for the modified system will be compared to a second OMA test on the modified system

• Steel and Composite Structures
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• v.34 no.2
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• pp.241-260
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• 2020

This article presented a comprehensive model to study static buckling stability and associated mode-shapes of higher shear deformation theories of sandwich laminated composite beam under the compression of varying axial load function. Four higher order shear deformation beam theories are considered in formulation and analysis. So, the model can consider the influence of both thick and thin beams without needing to shear correction factor. The compression force can be described through axial direction by uniform constant, linear and parabolic distribution functions. The Hamilton's principle is exploited to derive equilibrium governing equations of unified sandwich laminated beams. The governing equilibrium differential equations are transformed to algebraic system of equations by using numerical differential quadrature method (DQM). The system of equations is solved as an eigenvalue problem to get critical buckling loads and their corresponding mode-shapes. The stability of DQM in determining of buckling loads of sandwich structure is performed. The validation studies are achieved and the obtained results are matched with those. Parametric studies are presented to figure out effects of in-plane load type, sandwich thickness, fiber orientation and boundary conditions on buckling loads and mode-shapes. The present model is important in designing process of aircraft, naval structural components, and naval structural when non-uniform in-plane compressive loading is dominated.

• Smart Structures and Systems
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• v.24 no.2
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• pp.233-242
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• 2019

In this paper, an inverse approach based on uniform load surface (ULS) is presented for structural damage localization and quantification. The ULS is excellent approximation for deformed configuration of a structure under distributed unit force applied on all degrees of freedom. The ULS make use of natural frequencies and mode shapes of structure and in mathematical point of view is a weighted average of mode shapes. An objective function presented to damage detection is discrepancy between the ULS of monitored structure and numerical model of structure. Solving this objective function to find minimum value yields damage's parameters detection. The teaching-learning based optimization algorithm has been employed to solve inverse problem. The efficiency of present damage detection method is demonstrated through three numerical examples. By comparison between proposed objective function and another objective function which make use of natural frequencies and mode shapes, it is revealed present objective function have faster convergence and is more sensitive to damage. The method has good robustness against measurement noise and could detect damage by using the first few mode shapes. The results indicate that the proposed method is reliable technique to damage detection in structures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2541-2549
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• 2002

In order to study the vibration characteristics of fluid-structure interaction problem, two rectangular plates coupled with bounded fluid were investigated. Experimental modal analyses were carried out to extract the modal parameters of the system. Additionally. finite element modal analyses performed using a commercial computer code, ANSYS. The FEM solutions were compared with the experimental solutions to verify the finite element model. As a result, the comparison between the experiment and FEM results showed excellent agreement. The transverse vibration modes, in-phase and out-of-phase, were observed alternately in the fluid-coupled system. The thickness effect of the plates on the fluid-coupled natural frequencies and mode shapes was investigated for two different cases with the identical thickness and the unequal thickness. It was found that the coupled natural frequencies increase with the thickness for the identical plates regardless of the mode phase. The experimental and the finite element analysis results showed that the out-of-phase mode shapes were deviated from the symmetrical mode shapes in the plate transverse direction fur the unequal plate thickness case.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.4
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• pp.191-197
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• 1998

This paper described the dynamic characteristics of 20-story apartment buildings from the results of full-scale measurements and analysis. The natural frequencies and mode shapes are quantified by measuring and analyzing ambient vibrations of the structure and compared with the results from dynamic analysis. Comparison with computed mode shapes and frequencies shows good agreement with the experimental results. It proved that it is important to estimate coupling beam and soil parameters through a comparison of the measured results with calculated results.