The surface variational principle applied to an acoustic cavity

This paper presents the development and application of the Surface Variational Principle (SVP) for the evaluation of axisymmetric interior acoustic domains. The interior form of the SVP is first developed in the same manner as the existing exterior form. Then, the surface pressure and normal velocity are represented with a Ritz expansion using basis functions that span the entire wetted surface of the object of interest. The resultant formulation is used to analyze the interior acoustic response of a harmonically forced, right circular elastic cylinder. This validation model was chosen as both the structural and acoustic responses can be solved analytically. Results are presented for two models: one with a length to radius ratio of 2.4, and another with a ratio of 12.3. The SVP is shown to well reproduce the analytical solution for this geometry, and displays the asymptotic convergence expected of its variational formulation. The SVP formulation developed here is not restricted to right-circular cylindrical geometries, and may, indeed, be readily applied to any axisymmetric body.