SPURIOUS EIGENSOLUTIONS AND ITS TREATMENT IN BIEM AND BEM

Abstract

Spurious eigensolutions of the Laplace operator for annular problems was pointed out by Kitahara when the BIEM and BEM are employed to solve the eigenproblem. Later, Chen et al. treated this problem by using some remedies. The spurious eigensolution also appears for the biharmonic operator in the plate vibration. In this lecture, we demonstrate the occurrence of the spurious eigenvalues in the direct BEM, the null-field integral equation method and the fictitious BEM. Both the continuous formulation (BIEM) and discrete system (BEM) are discussed through an annular case. Three remedies, Burton & Miller approach, SVD updating technique and CHIEF concept, are employed to filter out the spurious eigenvalues. Numerical examples of annular plates and membranes are demonstrated to show the appearance of the spurious eigenvalues and the efficiency of the proposed remedies.