The hybrid boundary element method in structural acoustics

This paper presents a new symmetric formulation for structural acoustics in the frequency domain. Usually, the structural domain is discretized with the Finite-Element Method (FEM), whereas the Boundary Element Method (BEM) is used for the treatment of the infinite acoustic domain. Coupling formulations generally suffer from the dense and unsymmetric equation system of the BEM. To circumvent this drawback, the acoustic domain is discretized here with the Hybrid Stress Boundary Element Method (HSBEM), which is based on a variational principle. The discretized formulation consists of a symmetric stiffness-type equation based on a dynamic flexibility matrix in frequency domain. The HSBEM is thus easily coupled with other symmetric discretization methods, combining the advantages of a boundary formulation and a symmetric approach. An issue of the method is the evaluation of the flexibility matrix. This contribution extends former publications of the authors by a detailed analysis of the implementation of this matrix, leading to a new clustering scheme for an efficient treatment, based on the special structure of the integral kernel. Moreover, the treatment of hyper-singular integral kernels without integration, based on orthogonality properties for interior and exterior. domains is outlined. Examples show the consistency of this approach. Finally, a coupled formulation for structural acoustics employing the HSBEM for the structure and the acoustic domain is introduced. Several numerical tests elucidate the applicability of the method and the proposed improvements. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.