Determination of spurious eigenvalues and multiplicities of true eigenvalues in the dual multiple reciprocity method using the singular-value decomposition technique

Abstract

The dual multiple reciprocity method (MRM) has been employed by the authors' group [3] to solve the acoustic modes of a cavity with or without a thin partition. In this paper, we propose the singular-value decomposition technique to filter our spurious eigenvalues and to determine the multiplicity of true eigenvalues by combining the dual equations in MRM. Also, the role of the dual MRM for problems with a degenerate boundary is examined. Four examples, including a square cavity with multiple eigenvalues, a rectangular cavity, a rectangular cavity with a zero thickness partition and a rectangular cavity with a partition with finite thickness, are presented to demonstrate the validity of the proposed method. Also, the analytical solution if available, the finite element method results obtained by Petyt et al. and by ABAQUS and experimental measurements are compared with those of the proposed method, and it is found that the agreement between them is very good.