• Journal of KSNVE
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• v.4 no.3
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• pp.283-295
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• 1994

This work presents the experimental and finite element analysis results for the free vibration of 4 edges clamped, isotropic square plates with 2 collinear circular holes. Natural frequencies of finite element analysis are obtained for the complete square plate, the square plates with a central circular hole and the square plates with 2 collinear circulare holes. And natural frequencies are experimentally measured for the complete square plate, the square plate with a central circular hole(d = 150 mm) and the square plates with 2 collinear circular holes. Agreement between experimental and FEM results is excellent. Mode shapes in special case are presented. The conclusions of the study are as follows. There is little variation of nondimensional frequency parameters for the first six mode when the aspect ratio of circular hole is less than 1/6 in the isotropic square plates with 2 collinear circular holes. And the first nondimensional frequency parameter doesn't vary as the aspect ratio of circular hole increase.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.419-422
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• 2005

Global bifurcations and chaos in modal interactions of an imperfect circular plate with one-to-one internal resonance are investigated. The case of primary resonance, in which an excitation frequency is near natural frequencies, is considered. The damping force is not included in the analysis. The renormalization-group technique for KAM tori is used to obtain the criteria for large-scale stochasticity in the system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.504-514
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• 2003

We investigate global bifurcation in the subharmonic motion of a circular plate with one-to-one internal resonance. A system of autonomous equations are obtained from the partial differential equations governing the system by using Galerkin's procedure and the method of multiple scales. A perturbation method developed by Kovacic and Wiggins is used to find Silnikov type homoclinic orbits. The conditions under which the orbits occur are obtained.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.287-296
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• 2003

We investigate global bifurcation in the motion of an harmonically excited circular plate with one-to-one internal resonance. A perturbation method developed by Kovacic and Wiggins is used. Silnikov type homoclinic orbit has been pursued but it has turned out not to exist.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.140-144
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• 2004

Global bifurcations and chaos in modal interactions of an imperfect circular plate with one-to-one internal resonance are investigated. The case of primary resonance, in which an excitation frequency is near natural frequencies, is considered. The damping force is not included in the analysis. The Melnikov's method for heteroclinic orbits of the autonomous system was used to obtain the criteria for chaotic motion.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.8 s.101
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• pp.968-974
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• 2005

An analytical method for the hydroelastic vibration of a vessel composed of an upper annular plate and a lower circular plate is developed by the Rayleigh-Ritz method. The two plates are clamped along a rigid cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the plates is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid 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 well the fluid-coupled natural frequencies comparing with the finite element analysis result.

• 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.

• Structural Engineering and Mechanics
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• v.21 no.2
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• pp.169-184
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• 2005

This study deals with the free vibration of a circular plate in contact with a fluid; submerged in fluid, beneath fluid or on fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. The proposed method is verified by the finite element analysis using commercial program with a good accuracy. The normalized natural frequencies are obtained in order to estimate the relative added mass effect of fluid on each vibration mode of the plate. Also, the location of plate coupled with fluid and the cases of free and bounded fluid surface are studied for the effect on the vibration characteristics.

• Steel and Composite Structures
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• v.49 no.6
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• pp.713-728
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• 2023

This paper aims to investigate the free vibration analysis of FG plates, taking into account the effects of even and uneven porosity. The study employs the Hellinger-Reisner functional and obtains the element's bending stress and membrane stress fields from the analytical solution of the governing equations of the thick plate and plane problem, respectively. The displacement field serves as the second independent field. While few articles on free vibration analysis of circular plates exist, this paper investigates the free vibration of both rectangular and circular plates. After validating the proposed element, the paper investigates the effects of porosity distributions on the natural frequency of the FG porous plate. The study calculates the natural frequency of thin and thick bending plates with different aspect ratios and support conditions for various porosity and volume fraction index values. The study uses three types of porosity distributions, X, V, and O, for the uneven porosity distribution case. For O and V porosity distribution modes, porosity has a minor effect on the natural frequency for both circular and rectangular plates. However, in the case of even porosity distribution or X porosity distribution, the effect of porosity on the natural frequency of circular and rectangular plates increases with an increase in the volume fraction index.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.73-80
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• 2006

In order to examine the validity of an asymptotic solution for nonlinear interaction in asymmetric vibration modes of a perfect circular plate, we obtain the numerical solution. The motion of the plate is governed by nonlinear partial differential equation. The initial and boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution. It is found that traveling waves relating clockwise and counterclockwise as well as standing wave are depicted by the numerical solution.