Dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition

Abstract

The dual formulation of the multiple reciprocity method (MRM) is employed to solve the acoustic mode of a cavity with a thin partition. In order to avoid the spurious eigenvalues and non-uniqueness of the solution in the case of zero thickness for the partition, the hypersingular equation for MRM is considered. To determine the invariant quantity of influence coefficients more efficiently, an objectivity concept, i.e., a frame of indifference, is used by means of co-ordinate transformation. A generalized eigenvalue problem is derived and transformed into a standard eigenvalue problem through the state–space formulation. The spurious roots in MRM are examined and filtered out by using the hypersingular formulation. Three examples, including finite thickness of the partition, zero thickness and no partition, are shown to check the validity of the proposed method. Also, the analytical solution if available, the FEM results obtained by Petyt 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.