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Dispersion analysis of stabilized finite element methods for acoustic fluid interaction with Reissner–Mindlin plates
Author(s) -
Thompson Lonny L.,
Sankar Sridhar
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.133
Subject(s) - finite element method , method of mean weighted residuals , discretization , wavenumber , galerkin method , dispersion (optics) , mathematical analysis , vibration , coupling (piping) , mathematics , residual , mechanics , acoustics , physics , materials science , structural engineering , engineering , optics , algorithm , metallurgy
The application of stabilized finite element methods to model the vibration of elastic plates coupled with an acoustic fluid medium is considered. A complex‐wavenumber dispersion analysis of acoustic fluid interaction with Reissner–Mindlin plates is performed to quantify the accuracy of stabilized finite element methods for fluid‐loaded plates. Results demonstrate the improved accuracy of a recently developed hybrid least‐squares (HLS) plate element based on a modified Hellinger–Reissner functional, consistently combined with residual‐based methods for the acoustic fluid, compared to standard Galerkin and Galerkin gradient least‐squares plate elements. The technique of complex wavenumber 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 fluid and coupling matrices resulting from consistent implementation of pressure loading in the residual for the plate equation is examined and clarified for the different finite element approximations. Copyright © 2001 John Wiley & Sons, Ltd.