Eigensolutions of multiply connected membranes using the method of fundamental solutions

Abstract

In this paper, the method of fundamental solutions (MFS) of single and double-layer potential approaches for solving the eigenfrequencies of multiply connected membranes is proposed. By employing the fundamental solution, the coefficients of influence matrices are easily determined. The spurious eigensolution accompanied by 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 kernels and circulants for an annular membrane. In order to obtain the true eigensolution, the singular value decomposition (SVD) updating techniques and the Burton and Miller method are utilized to filter out the spurious eigensolutions. Two examples are demonstrated analytically and numerically to see the validity of the present method.