True and spurious eigensolutoins for membrane and plate problems by using method of fundamental solutions

Abstract

In this paper, the method of fundamental solutions is utilized to solve free vibration of membrane and plate problems. Single and double-layer potential approaches are both considered for the membrane problem and 6 (C4 2) options by adopting two potentials from the single, double, triple and quadruple potentials are chosen for the plate problem. Spurious eigenvalues appear in the method of fundamental solution for the multiply-connected domain. The occurring mechanism of the spurious eigenvalues for membrane and plate problems is studied analytically by an annular case. The degenerate kernels and circulants are utilized to derive the true and spurious eigenequations analytically in the discrete model. True eigenequation depends on the boundary condition while spurious eigenequation relies on the formulation. The remedy, Burton & Miller method, is employed to suppress the occurrence of the spurious eigenvalues. Two examples are demonstrated to check the validity of the present formulations.