Complex Wave-number Dispersion Analysis of Stabilized Finite Element Methods for Acoustic Fluid – Structure Interaction

The application of finite element methods to problems in structural acoustics ( the vibration of an elastic body coupled to an acoustic fluid medium) is considered. New stabilized methods based on the Hellinger-Reissner variational principle with a generalized least-squares modification are developed which yield improvement in accuracy over the standard Galerkin finite element method for both in vacuo and acoustic fluid-loaded Reissner-Mindlin plates. Through judicious selection of design parameters this formulation provides a consistent framework for enhancing the accuracy of mixed Reissner-Mindlin plate elements that have no shear locking or spurious modes. Combined with Galerkin Least-Squares (GLS) methods for the acoustic fluid, the method presents a new framework for accurate modeling of acoustic fluid-loaded structures. The technique of complex wave-number dispersion analysis is used to examine the accuracy of the discretized system in the representation of free-waves for fluid-loaded plates. Improved methods are designed such that the finite element dispersion relations closely match each branch of the complex wavenumber loci for fluid-loaded plates. Comparisons of finite element dispersion relations demonstrate the superiority of the new hybrid least-squares (HLS) plate elements combined with GLS methods for the fluid over standard Galerkin and Galerkin Gradient Least-Squares (GGLS) finite element methods.