ON THE FORMULATION OF THE ACOUSTIC BOUNDARY ELEMENT EIGENVALUE PROBLEMS

Acoustic algebraic eigenvalue analysis by the Boundary Element Method (BEM) can be formulated by the Dual Reciprocity Method (DRM) of Nardini and Brebbia or by the Complementary Function-Particular Integral Method (PIM) proposed by Ahmad and Banerjee. But both DRM and PIM require inversion of a matrix of size at least as large as the system matrices before the equations can be cast in the form of generalized eigensystem. This makes these methods inefficient for large problems of practical interest. In this paper, a rather simple technique is proposed which eliminates the need to invert any matrix in the process of setting up the algebraic eigenvalue problem, especially for the most important case where all the boundary walls are acoustically hard (partial-P/partial-n = 0). A few example problems having known analytical and experimental results are solved in order to demonstrate the validity of the new technique. It is also demonstrated that, unlike in elasticity, here the boundary element domain must be adequately zoned or an adequate number of internal points must be incorporated in order to solve truly 2-D or 3-D problems.