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Method of Fundamental Solutions for Plate Vibrations in Multiply Connected Domains

Published online by Cambridge University Press:  05 May 2011

C. C. Tsai ,
D. L. Young  and
C. M. Fan
C. C. Tsai*
Affiliation:
Department of Information Technology, Toko University, Chia-Yi County, Taiwan 61363, R.O.C.
D. L. Young*
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
C. M. Fan*
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
* Assistant Professor
**Professor
***Postdoctoral Fellow
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Abstract

This paper develops the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations of multiply connected domains. The complex-valued MFS combined with the mix potential method are utilized in order to avoid the spurious eigenvalues. The benchmarked problems of annular plates with clamped, simply supported and free boundary conditions are studied analytically as well as numerically. Wherein the results demonstrate that all true eigenvalues are contained and no spurious eigenvalues are included. In the analytical studies, the continuous version of the MFS is utilized to obtain the eigenequation by applying the degenerate kernels and Fourier series. The proposed numerical method is free from singularities, meshes, and numerical integrations and thus can be easily utilized to solve plate vibrations free from spurious eigenvalues in multiply connected domains.

Keywords

Method of fundamental solutionsMix potential methodPlate vibrationSpurious eigenvaluesAnnular plateClampedSimply supportedFree boundary conditions
Type
Articles
Information
Journal of Mechanics , Volume 22 , Issue 3 , September 2006 , pp. 235 - 245
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

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