Mathematical analysis of true and spurious eigenvalues for annular plates using the method of fundamental solutions

Abstract

In this paper, the method of fundamental solutions (MFS) for solving the eigenfrequencies of an annular plate is proposed. By employing the fundamental solutions, the coefficients of influence matrices are easily determined. Spurious eigensolutions in conjunction with the eigensolutions appear. It is found that spurious eigensolutions using the MFS depend on the location of the inner boundary where fictitious sources are distributed. To verify this finding, true and spurious eigenvalues for an annular plate are analytically studied using degenerate kernels and circulants. In order to obtain the true eigensolution, the singular value decomposition (SVD) updating technique and the Burton & Miller method are utilized to filter out the spurious eigensolutions. An annular plate is demonstrated analytically to see the validity of the present method.