Abstract
The application of stabilized finite element methods to model the vibration of elastic plates coupled with 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 Galerkin and Galerkin Generalized Least Squares (GGLS) finite element methods 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. Combined with stabilization 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. The influence of different finite element approximations for the fluid-loaded plate system are examined and clarified. 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 hybrid least-squares (HLS) plate elements combined with stabilized methods for the fluid over standard Galerkin methods with mixed interpolation and shear projection (MITC4) and GGLS methods.