Revisit of the degenerate scale for plate problems

Abstract

Degenerate scale occurs once the boundary integral equation (BIE) is employed to solve plate problems. There are two ways to be considered. First, the degenerate kernel for expressing the closed-form fundamental solution is utilized to study the occurring mechanism for circular and elliptical plates using polar and elliptical coordinates, respectively. Second, the BIE is discretized and reformulated to a 4 by 4 eigenproblem to obtain degenerate scales instead of the direct-searching scheme. Analytical degenerate scales for the circular and elliptical shapes are obtained while numerical results for general shapes are also considered.