# FREE VIBRATION ANALYSIS OF MULTIPLY CONNECTED PLATES USING THE METHOD OF FUNDAMENTAL SOLUTIONS

• Ying-Te Lee
• Jeng-Tzong Chen
• I-Lin Chen
Conference paper

## Abstract

In this paper, the method of fundamental solutions (MFS) for solving the eigenfrequencies of multiply connected plates is proposed. The coefficients of influence matrices are easily determined when the fundamental solution is known. True and spurious eigensolutions appear at the same time. It is found that the spurious eigensolution using the MFS depends on the location of the inner boundary where the fictitious sources are distributed. To verify this finding, mathematical analysis for the appearance of spurious eigenequations using degenerate kernels and circulants is done by demonstrating an annular plate with a discrete model. In order to obtain the true eigensolution, the Burton & Miller method is utilized to filter out the spurious eigensolutions. One example is demonstrated analytically and numerically to see the validity of the present method.

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### REFERENCES

1. 1.
V.D. Kupradze (1964), A method for the approximate solution of limiting problems in mathematical physics. Computational Mathematics and Mathematical Physics, 4, pp. 199–205.
2. 2.
G. Fairweather and A. Karageorghis (1998), The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics, 9, pp. 69–95.
3. 3.
C.S. Chen, M.A. Golberg and Y.C. Hon (1998), The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations. International Journal for Numerical Methods in Engineering, 43, pp. 1421–35.
4. 4.
A. Karageorghis (2001), The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation. Applied Mathematics Letters, 14, pp. 837–42.
5. 5.
J.T. Chen, S.Y. Lin, K.H. Chen and I.L. Chen (2004), Mathematical analysis and numerical study of true and spurious eigenequations for free vibration of plates using real-part BEM. Computational Mechanics, 34, pp. 165–180.
6. 6.
J.T. Chen, L.W. Liu and H.-K. Hong (2003), Spurious and true eigensolutions of Helmholtz BIEs and BEMs for a multiply-connected problem. In Proceedings of the Royal Society London Series A, 459, pp.1891–925.
7. 7.
J.T. Chen, I.L. Chen and Y.T. Lee (2004), Eigensolutions of multiply-connected membranes using the method of fundamental solutions. Engineering Analysis with Boundary Elements, Revised.Google Scholar
8. 8.
W. Leissa (1969), Vibration of Plates. NASA SP-160.Google Scholar