• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.647-651
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• 2002

This study dealt with the free vibration of two identical rectangular plates coupled with fluid. In order to investigate the vibration characteristics of fluid-coupled rectangular plates, an analytical method based on the finite Fourier series expansion and Rayleigh-Ritz method was suggested. A commercial computer code, ANSYS was used to perform finite element analysis and we investigated the vibration characteristics with mode shapes and natural frequencies. As a result, the transverse vibration modes, in-phase and out-of-phase, were observed alternately in the fluid-coupled system. The effect of fluid bounding and plate boundary condition on the fluid-coupled natural frequency were investigated. It was shown that the mode numbers increased, the normalized natural frequencies monotonically increased.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.9
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• pp.439-453
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• 2001

This study deals with the free vibration of two identical circular plates coupled with a bounded fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. In the theory, it is assumed that the ideal fluid in a rigid cylindrical container and the two plates are clamped along the plate edges. The proposed method is verified by the finite element analysis using commercial program with a good accuracy. Two transverse vibration modes, namely in-phase and out-of-phase, are observed alternately in the fluid-coupled system when the number of nodal circles increases for the fixed nodal diameter. The effect of gap between the plates on the fluid-coupled natural frequencies sis also investigated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.1
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• pp.123-130
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• 2008

An analytical method for the free vibration of a flexible rectangular plate in contact with water is developed by the Rayleigh-Ritz method. The plate clamped along the edges is partially contacted with water at both sides. It is assumed that the contained water is incompressible and inviscid. The wet mode shape of the plate is assumed as a combination of the dry mode shapes of a clamped beam. The liquid motion is described by using the liquid displacement potential and determined by using the compatibility conditions along the liquid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict excellently the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.3
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• pp.207-215
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• 2015

This paper deals with a theoretical method to calculate natural frequencies of a fixed-free rectangular tank partially in contact with an outer water gap. Orthogonal polynomials satisfying the boundary conditions of the tank are used as admissible functions in the Rayleigh-Ritz method. A quarter model of the liquid-coupled system is constructed and it is simplified to a line supported flat plate in contact with the liquid. The liquid displacement potential functions satisfying the Laplace equation and water boundary conditions are derived, and the finite Fourier transform is accomplished in conjunction with the compatibility requirement along the contacting interfaces between the tank and water. An eigenvalue problem is derived so that the natural frequencies of the wet rectangular tank can be extracted. The predictions from the proposed analytical method show good agreement with the finite element analysis results.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.134-144
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• 1993

Sandwich plate is consisted of equal two isotropic, thin, stiff and strong sheets of dense material separated symmetrically by an isotropic thick layer which may be much less stiff and strong. This study analyzed the dependency of the natural frequencies and mode shapes of sandwich plates on material properties, thicknesses of faces and cores, and various boundary conditions using Rayleigh-Ritz method. E-glass Woven Roving and another two kinds of materials were selected as a face, P.V.C. and another kinds of materials were selected as a core. Natural frequencies and mode shapes obtained by Rayleigh-Ritz method were compared with F.E.M. solutions using ADINA program.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1485-1492
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• 1992

While the vibration of circular plates were considered by many researchers, rather less attention is given to elliptical plates. In the present paper, the Rayleigh-Ritz mothod is used to obtain an eigenvalue equation for the free flexural vibration of thin elliptical plates having the classical free, simply suported or clmped boundary condition. Circular plates are included as a special case of the elliptical plates. Products of simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals. The analysis is developed for rectilinear orthotropic plates but the numerical results are given for isotropic plates with various aspect ratios.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.611-617
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• 1986

In this paper, it is attempted to derive the minimum torque as the optimal value on each joint, which is applied during a PTP-motion in the range of working area of a supposed industrial robot. The rupposed industrial robot consits of 3-R joints prepared on three links, The optimizational analysis is performed by the formulation of a variational calculus process due to Rayleigh-Ritz method. That is, the torques of the inverse dynamic problem on joints in a arbitrary positions are computed by a generalized inertia matrix method.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.1
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• pp.158-172
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• 1992

In ships and offshore structures, there are many local structures formed of thick plates and/or having the form of double wall panels. For the vibration analysis of such a kind of structures, Mindlin plate theory which includes the effects of shear deformation and rotary inertia is usually adopted. In this paper, the vibration and dynamic sensitivity analysis of Mindlin plates having the boundary conditions elastically restrained against rotation have been accomplished using the Rayleigh-Ritz method. Polynomials having the property of the Timoshenko beam functions are introduced and used as trial functions in the spatial representation of the deflection and rotations of cross sections in two directions of the plates. The results obtained by the introduced polynomials gave nearly the same numerical results as those by the Timoshenko beam functions with the remarkable reduction of computational efforts especially in the dynamic sensitivity analysis.

• Proceedings of the Korean Nuclear Society Conference
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• 2004.10a
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• pp.953-954
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• 2004

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.6
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• pp.1363-1370
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• 1995

A nonlinear dynamic modeling method for simply supported structures undergoing large overall motion is suggested. The modeling method employs Rayleigh-Ritz mode technique and Von Karman nonlinear strain measures. Numerical study shows that the suggested modeling method provides qualitatively different results from those of the Classical Linear Cartesian modeling method. Especially, natural frequency variations and residual deformation due to membrane strain effects are observed in the numerical results obtained by the suggested modeling method.