A weakly singular boundary integral equation in elastodynamics for heterogeneous domains mitigating fictitious eigenfrequencies

Abstract

A boundary element formulation applied to dynamic soil–structure interaction problems with embedded foundations may give rise to inaccurate results at frequencies that correspond to the eigenfrequencies of the finite domain embedded in an exterior domain of semi-infinite extent. These frequencies are referred to as fictitious eigenfrequencies. This problem is illustrated and mitigated modifying the original approach proposed by Burton and Miller for acoustic problems, which combines the boundary integral equations in terms of the displacement and its normal derivative using a complex coupling parameter α. Hypersingular terms in the original boundary integral equation are avoided by replacing the normal derivative by a finite difference approximation over a characteristic distance h, still leading to an exact boundary integral equation. A proof of the uniqueness of this formulation for small h and a smooth boundary is given, together with a parametric study for the case of a rigid massless cylindrical embedded foundation. General conclusions are drawn for the practical choice of the dimensionless coupling parameter α ¯ and the dimensionless distance h ¯ .