| The application of finite element methods to problems in structural acoustics (the vibration of an elastic structure coupled to an acoustic medium) is considered. New methods are developed which yield dramatic improvement in accuracy over the standard Galerkin finite element approach. The goal of the new methods is to decrease the computational burden required to achieve a desired accuracy level at a particular frequency thereby enabling larger scale, higher frequency computations for a given platform.;A new class of finite element methods, Galerkin Generalized Least-Squares (GGLS) methods, are developed and applied to model the in vacuo and fluid-loaded vibration response of Reissner-Mindlin plates. Through judicious selection of the design parameters inherent to GGLS methods, this formulation provides a consistent framework for enhancing the accuracy of finite elements. An optimal GGLS method is designed such that the complex wave-number finite element dispersion relations are identical to the analytic relations. Complex wave-number dispersion analysis and numerical experiments demonstrate the dramatic superiority of the new optimal method over the standard finite element approach for coupled and uncoupled plate vibrations. The new method provides for a dramatic decrease in discretization requirements over previous methods.;The canonical problem of a baffled, fluid-loaded, finite cylindrical shell is also studied. The finite element formulation for this problem is developed and the results are compared to an analytic solution based on an expansion of the displacement using in vacuo mode shapes. A novel high resolution parameter estimation technique, based on Prony's method, is used to obtain the complex wave-number dispersion relations for the finite structure. The finite element dispersion relations enable the analyst to pinpoint the source of errors and form discretization rules. The stationary phase approximation is used to obtain the dependence of the far field pressure on the surface displacement. This analysis allows for the study of the propagation of errors into the far field as well as the determination of important mechanisms of sound radiation. |
