Improvement of Convergence Properties for Ritz Formulations of Acousto-Elasticity Problems

Many applications require the analysis of structures with cavities filled with fluids or gases. In many cases the fluid domains can be ignored, and we can safely assume that the structure’s in vacuo properties apply. Sometimes, however, resonances in the fluid can couple with structural resonances to yield acousto-elastic modes of response. The most popular approach to these problems is to describe the trapped fluid in terms of a finite number of eigenmodes of a geometrically identical cavity with rigid boundaries. Then, the structural and fluid domains are coupled by matching the pressure across the wetted surface. However, for light structures with embedded cavities of relatively heavy fluids such as water, this technique may not be satisfactory because the interior rigid-cavity modes are poor candidates to satisfy the “natural boundary conditions” that exist at the fluid-structure boundary. This paper explores the use of an expanded set of Ritz functions for the fluid domain, to include a number of functions that explicitly allow for motion along the wetted surface. The method is applied to a two-dimensional rectangular acoustic cavity, with rigid boundaries on all sides except for a flexible membrane on the top surface. Through comparisons with the “exact solution,” it is shown that the solution using the expanded set of Ritz functions converges more quickly than do solutions employing rigid cavity modes. The convergence trends of the first few natural frequencies are computed for a number of different physical and geometric system properties.Copyright © 2012 by ASME