Numerical experiments for acoustic modes of a square cavity using the dualboundary element method

The dual integral formulation for the Heimholtz equation for use in solving the acoustic modes of a two-dimensional square cavity is derived, and a ge neral dual boundary element method (BEM) program is developed. Numerical ex periments for the degenerate acoustic modes of a square cavity are performe d. It is found that the degenerate modes can be distinguished by specifying the normalized boundary data at different boundary points using either the singular integral equation (UT method) or the hypersingular integral equat ion (LM method). This technique can be employed to determine the multiplici ty of the eigenvalue. Two examples with Dirichlet and Neumann boundary cond itions are given to show the validity of the proposed technique. Sensitivit y and failure in determining the acoustic modes by specifying the normalize d data at the boundary locations near and on the node are examined, respect ively. Also, numerical results are obtained using finite element method (FE M) and analytical solutions for comparison. Good agreement between them is obtained. (C) 1998 Elsevier Science Ltd. All rights reserved.