Dual integral formulation for acoustic resonances of a two-dimensional damped cavity with a thinpartition

Abstract

This paper derives a dual integral formulation for the Helmholtz equation used to analyze the problem of the acoustic resonances for a damped cavity with a thin, incomplete partition. The presence of damping in the medium results in the incorporation of complex wave numbers in the Helmholtz equation within mathematical models. To address the singular and hypersingular integrals of the four complex-valued wave number kernel functions, the addition theorem is employed to expand them into series representations involving only real wave number. After then, the singular and hypersingular integrals are successfully transformed into a summation of regular integrals in an infinite series using the proposed regularization technique. This study investigates the acoustic resonances of a cavity with a thin partition, focusing on the effect of damping on these resonances. A case with an exact solution is given as a standard benchmark to evaluate the convergence and accuracy of the proposed dual integral equation. Finally, two numerical examples, involving rectangular and submarine-shaped cavities with a thin, incomplete partition, are presented. The acoustic frequencies and modes are determined using the developed program.