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

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 techn ique to filter our spurious eigenvalues and to determine the multiplicity o f true eigenvalues by combining the dual equations in MRM. Also, the role o f the dual MRM for problems with a degenerate boundary is examined. Four ex amples, including a square cavity with multiple eigenvalues, a rectangular cavity, a rectangular cavity with a zero thickness partition and a rectangu lar cavity with a partition with finite thickness, are presented to demonst rate the validity of the proposed method. Also, the analytical solution if available, the finite element method results obtained by Petyt er al. and b y ABAQUS and experimental measurements are compared with those of the propo sed method, and it is found that the agreement between them is very good. ( C) 2000 Academic Press.