Dispersion Analysis of Stabilized Finite Element Methods
for Acoustic Fluid - Structure Interaction
Lonny L. Thompson and Sridhar Sankar
Advanced Computational Mechanics Research Laboratory
Department of Mechanical Engineering and Engineering Mechanics
Clemson University
Clemson, South Carolina 29634-0921
NCA-Vol. 27, Proceedings of the ASME Noise Control and Acoustics Division - 2000, ASME 2000, pp. 39--50;
2000 International Mechanical Engineering Congress and Exposition,
Symposium on Computational Acoustics,
Nov. 5-10, 2000, Orlando, Florida.
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.
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