A New Design Sensitivity Analysis of Acoustic Problems Based on Bem Avoiding Fictitious Eigenfrequency Issue

Abstract

This paper presents a new design sensitivity analysis based on the boundary element method avoiding the fictitious eigenfrequency issue in acoustic problems. The direct differentiation method is applied to the derivation of sensitivity formulas. In solving an external acoustic problem with internal sub-domains by means of the boundary integral equation without any care, is numerical solution is violated at the so-called fictitious eigenfrequencies corresponding to the internal subdomains. The present paper proposes a new boundary element sensitivity analysis avoiding such a fictitious eigenfrequency problem. This is based on the dual boundary integral equation, proposed previously by the authors, and the integral expressions are differentiated directly with respect to the design parameters. One equation is the combined boundary integral equation proposed by Burton-Miller and the other is the normal derivative boundary integral equation multiplied by the same coupling parameter as in the Burton-Miller expression. The quadrilateral element is employed in this study. The Burton-Miller integral expression is used only at the middle nodes of element, while the normal derivative boundary integral equation multiplied by the same coupling parameter is applied to the vertex nodes of element, and vice versa. The effectiveness of the proposed approach is illustrated through some numerical examples for three-dimensional problems.