Open Access

ARTICLE

The Method of Fundamental Solutions for Eigenfrequencies of Plate Vibrations

D.L. Young^1,2, C.C. Tsai³, Y.C. Lin¹, C.S. Chen⁴

1 Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei, 10617 Taiwan
2 Correspond to: D.L. Young, E-mail: dlyoung@ntu.edu.tw
3 Department of Information Technology, Toko University, Chia-Yi County, 61363 Taiwan
4 Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA

Computers, Materials & Continua 2006, 4(1), 1-10. https://doi.org/10.3970/cmc.2006.004.001

Abstract

This paper describes the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations by utilizing the direct determinant search method. The complex-valued kernels are used in the MFS in order to avoid the spurious eigenvalues. The benchmark problems of a circular plate with clamped, simply supported and free boundary conditions are studied analytically as well as numerically using the discrete and continuous versions of the MFS schemes to demonstrate the major results of the present paper. Namely only true eigenvalues are contained and no spurious eigenvalues are included in the range of direct determinant search method. Consequently analytical derivation is carried out by using the degenerate kernels and Fourier series to obtain the exact eigenvalues which are used to validate the numerical methods. The MFS is free from meshes, singularities, and numerical integrations. As a result, the proposed numerical method can be easily used to solve plate vibrations free from spurious eigenvalues in simply connected domains.

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Keywords

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