On spurious eigenvalues of doubly-connected membrane

Abstract

Spurious eigensolutions in the boundary integral equation (BIE) or boundary element method (BEM) for the eccentric membrane are studied analytically and numerically in this paper. For the mathematical analysis, we use the null-field integral equation, the degenerate kernels and the Fourier series to prove the existence of spurious eigensolutions in the continuous system. Examples of eccentric case and general shape are solved by using the null-field equation approach and BEM, respectively. The spurious eigenvalue is found to be the true eigenvalue of a circular membrane with the inner radius. Also, the trivial outer boundary densities are found in case of spurious eigenvalues and are shown in the bar chart.