Eigensolution of annular membrane using the method of fundamental solutions

In this paper, the method of fundamental solutions (MFS) for solving the eigenfrequencies of annular membrane is proposed. By employing the fundamental solution, the coefficients of influence matrices are easily determined. The spurious eigensolution in conjunction with the true eigensolution appears. It is found that the spurious eigensolution using the MFS depends on the location of the inner boundary where the sources are distributed. To verify this finding, the true and spurious eigenvalues in an annular domain are analytically studied using the degenerate kernel and circulant. 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. One example is demonstrated analytically and numerically to see the validity of the present method