• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.2
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• pp.186-193
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• 2011

The NDIF method(non-dimensional dynamic influence function method) for free vibration analysis of arbitrarily shaped plates with the simply supported edge is newly developed in the paper. In order to extract the system matrix that gives the natural frequencies and natural modes of the plate of interest, the difficulty of measuring higher differential terms involved in the simply supported boundary condition is successfully overcome. Finally, the excellence of the characteristics of convergence and accuracy of the proposed method is shown through two verification examples, which indicate that natural frequencies and natural modes obtained by the proposed method are very accurate and swiftly converged even though a small number of nodes are used compared with FEM.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.921-925
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• 2003

An analytical method for the free vibration of single circular plate submerged in a fluid-filled rigid cylindrical vessel was developed by the Rayleigh-Ritz method based on the Fourier-Bessel series expansion. It was assumed that the plate is clamped at an offcentered location of the cylinder, and the non-viscous incompressible fluid contained in the cylinder is bisected by the plate. It was found that the theoretical results can predict well the fluid-coupled natural frequencies with excellent accuracy comparing with the finite element analysis results. The offcentered distance effect on the natural frequencies was also observed.

• Journal of Industrial Technology
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• v.29 no.A
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• pp.19-25
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• 2009

The proper orthogonal decomposition (POD) analysis of vibration of a steel frame structure is performed to extract modal parameters. The theoretical background of the POD method is introduced briefly, and this technique is further applied to free vibration displacements of one bay-two story steel frame structure to extract the modal parameters. From the POD analysis of the steel frame structure, it is found that important modal parameters such as true mode shapes, modal kinematic energy, natural frequencies, and damping ratios can be obtained for the building efficiently and in detail. Therefore, it is concluded that the POD method could be one of the useful techniques in analysis of vibration of structures.

• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.79-92
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• 2015

In this study, free vibration analyses of symmetric laminated cantilever and simply supported damaged composite beams are investigated by using finite element method (FEM). Free vibration responses of damaged beams are examined using Euler Bernoulli beam and classical lamination theories. A computer code is developed by using MATLAB software to determine the natural frequencies of a damaged beam. The local damage zone is assumed to be on the surface lamina of the beam by broken fibers after impact. The damaged zone is modeled as a unidirectional discontinuous lamina with $0^{\circ}$ orientations in this study. Fiber volume fraction ($v_f$), fiber aspect ratio ($L_f/d_f$), damage length ($L_D$) and its location (${\lambda}/L$), fiber orientation and stacking sequence parameters effects on natural frequencies are investigated. These parameters are affected the natural frequency values significantly.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.768-771
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• 2005

The purpose of this paper is to investigate the free vibration of stepped noncircular arches. Taking into account the effects of axial deformation, rotatory inertia and shear deformation, the governing differential equations are solved numerically for the elliptic and sinusoidal geometries with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. The lowest four natural frequencies are presented as functions of four non-dimensional system parameters: the arch rise to span length ratio, the slenderness ratio, the section ratio, and the discontinuous sector ratio.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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• pp.900-906
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• 2010

This note proposes vibration-free motor control through modified LQG/LTR methodology. A conventional LQG/LTR method is a design tool in the frequency domain. However, unlike the conventional one, the proposed one is a time response based design method. This feature is firstly designed by parameterized settling time control gain through the target loop design procedure and the feature is secondly realized by loop transfer recovery. In order to show convergence to the target loop transfer functions, asymptotic behaviors of the open and the closed loop transfer functions are shown. At the conclusion, it is verified that the proposed method is robustly stable to parametric uncertainties through ${\mu}$-plot.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.2
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• pp.192-199
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• 2009

This paper presents the free vibration analysis of a circular plate with a concentric square hole. The boundary condition is the edge of the square hole is free and the outer circular plate is simply supported. Due to the geometric abnormality, this analysis does not permit an exact solution. The present problem deals with the numerical calculation of the natural frequencies and mode shapes of vibration of the structure by independent coordinate coupling method(ICCM). The numerical results show the efficacy of the ICCM and changes in natural frequencies and modes due to the square hole size.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.6 s.123
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• pp.531-538
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• 2007

A new method for free nitration analysis using series functions is proposed to obtain the eigenvalues of arbitrarily shaped, polygonal plates with clamped edges. Since a general solution used in the method satisfies the equation of motion for the transverse vibration of a plate, the method offers very accurate eigenvalues, compared to FEM or BEM results. In addition, the method can minimize the amount of numerical calculation because it has the advantage of not needing to divide the plate of interest. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM (NASTRAN) or another analytical method.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.537-573
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• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Journal of Ocean Engineering and Technology
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• v.24 no.6
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• pp.61-70
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• 2010

This study presents free vibration analyses of perforates steel plates with various cutouts. Four different parameters (shape, size, curvature radius ratio, and rotation of cutouts) were considered to investigate the effects of those parameters on the free vibration characteristics, such as natural frequencies of the perforated steel plates. Three different shapes of cutouts are circle, square, and triangle, and the considered sizes are 5, 10, 15, 20, and 25 mm. For the triangular and square cutouts, the characteristic radii of the inscribed circles of those cutouts were defined. In addition, the curvature radius ratio was defined as the ratio of curvature radius of bluntness and the characteristic radius. Then, total seven different curvature radius ratios (0, 0.1, 0.3, 0.5, 0.7, 0.9, and 1) were considered. To investigate the rotation effect of the cutouts, it was considered four rotations ($0^{\circ}$, $15^{\circ}$, $30^{\circ}$, and $45^{\circ}$) for the square cutouts and three rotations (0, 15, and 30) for the triangular cutouts. All the free vibration analyses were conducted using a general purpose finite element program. From the analyses we found that the most influential parameter for the free vibration response of the perforated plates is the size of cutout. The other factors such as the shape, curvature radius ratio, and rotation are minors; they mainly change the natural frequency as long as the size effect is accompanied.