Determination of spurious eigenvalues and multiplicities of true eigenvalues using the real-part dual BEM

The complex-valued dual BEM has been employed by Chen and Chen (1998) to so lve the acoustic modes of a cavity with or without a thin partition. A nove l method using only the real part of the complex-valued dual BEM was found by Chen (1998) to be equivalent to the dual MRM. However, spurious eigenval ues occur. In this paper, we propose the singular value decomposition techn ique to filter out spurious eigenvalues and to determine the multiplicity o f true eigenvalues by combining the real-part dual equations. Also, the rol e of the real-part dual BEM for problems with a degenerate boundary is exam ined. Four examples, including a square cavity with multiple eigenvalues, a rectangular cavity, a rectangular cavity with a zero thickness partition a nd a rectangular cavity with a partition with finite thickness, are present ed to demonstrate the validity of the proposed method. Also, the analytical solution if available, the FEM results obtained by Petyt et al. and obtain ed using ABAQUS and the experimental measurements are compared with those o f the proposed method, and it is found that agreement between them is very good.