• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.10 s.115
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• pp.1024-1035
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• 2006

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (circumferentially closed), circular rings with an elliptical or circular cross-section. Displacement components $u_r,\;u_\theta\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the circular rings are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rings. Novel numerical results are presented for the circular rings having an elliptical cross-section based upon 3-D theory. Comparisons are also made between the frequencies from the present 3-D Ritz method and ones obtained from thin and thick ring theories, experiments, and another 3-D method.

• 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 KSR Conference
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• 2009.05a
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• pp.1083-1087
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• 2009

We present an 1-dimensional annular disk element with which natural vibration of a circular plate can be analyzed accurately and facilely. The natural vibration characteristics of a circular plate with free outer boundary are analyzed by using the presented I-dimensional element. Its results are compared with the results obtained by utilizing 2-dimensional 8-node quadrilateral plane element and cyclic symmetry of the circular plate. And also, by comparing with the theoretical results of previous researchers, the accuracy and facility of the presented I-dimensional element are verified.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.252-257
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• 2004

Free vibration of a semi-circular pipe conveying fluid is analyzed when the pipe is clamped at both ends. To consider the geometric non-linearity, this study adopts the Lagrange strain theory and the extensibility of the pipe. By using the extended Hamilton principle, the non-linear partial differential equations are derived, which are coupled to the in-plane and out-of\ulcornerplant: motions. To investigate the vibration characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies are computed from the linearized equations of motion in the neighborhood of the equilibrium position. From the results. the natural frequencies for the in-plane and out-of-plane motions are vary with the flow velocity. However, no instability occurs the semi-circular pipe with both ends clamped, when taking into account the geometric non-linearity explained by the Lagrange strain theory.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.258-262
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• 2004

An analytical method for the free vibration of two circular plates coupled with a fluid was developed by the Rayleigh-Ritz method. The two plates with unequal thickness and diameter are clamped along the 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 circular 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 a eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies with excellent accuracy comparing with the finite element analysis result.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.276-276
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• 2003

This paper dealt with an experimental study on the free vibration of circular-tube-beam submerged in water. A circular-tube-beam is commonly founded on the nuclear fuel assembly system in nuclear reactor. The nuclear fuel assembly susceptible to flow-induced vibration in nuclear reactor. So, the nuclear fuel assembly be designed to avoid any resonance due to the vibration during the reactor operation. In the experiment, applied boundary condition is clamped-free and the effect of water height to natural frequency and damping is studied. The experiment in air and in water has been performed. Used experimental method is impact exciting method. The natural frequencies and damping ratio according to water height is presented.

• 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.

• 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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• 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.