Finite element analysis of the vibration problem of a plate coupled with a fluid

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We consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid. The plate is modelled by Reissner-Mindlin equations while the fluid is described in terms of displacement variables. This formulation leads to a symmetric eigenvalue problem. Reissner-Mindl...

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Autor principal: Duran, Ricardo Guillermo
Publicado: 2000
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0029599X_v86_n4_p591_Duran
http://hdl.handle.net/20.500.12110/paper_0029599X_v86_n4_p591_Duran
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_0029599X_v86_n4_p591_Duran2023-06-08T14:55:29Z Finite element analysis of the vibration problem of a plate coupled with a fluid Duran, Ricardo Guillermo We consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid. The plate is modelled by Reissner-Mindlin equations while the fluid is described in terms of displacement variables. This formulation leads to a symmetric eigenvalue problem. Reissner-Mindlin equations are discretized by a mixed method, the equations for the fluid with Raviart-Thomas elements and a non conforming coupling is used on the interface. In order to prove that the method is locking free we consider a family of problems, one for each thickness t > 0, and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t → 0. We prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t. © Springer-Verlag 2000. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2000 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0029599X_v86_n4_p591_Duran http://hdl.handle.net/20.500.12110/paper_0029599X_v86_n4_p591_Duran
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid. The plate is modelled by Reissner-Mindlin equations while the fluid is described in terms of displacement variables. This formulation leads to a symmetric eigenvalue problem. Reissner-Mindlin equations are discretized by a mixed method, the equations for the fluid with Raviart-Thomas elements and a non conforming coupling is used on the interface. In order to prove that the method is locking free we consider a family of problems, one for each thickness t > 0, and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t → 0. We prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t. © Springer-Verlag 2000.
author Duran, Ricardo Guillermo
spellingShingle Duran, Ricardo Guillermo
Finite element analysis of the vibration problem of a plate coupled with a fluid
author_facet Duran, Ricardo Guillermo
author_sort Duran, Ricardo Guillermo
title Finite element analysis of the vibration problem of a plate coupled with a fluid
title_short Finite element analysis of the vibration problem of a plate coupled with a fluid
title_full Finite element analysis of the vibration problem of a plate coupled with a fluid
title_fullStr Finite element analysis of the vibration problem of a plate coupled with a fluid
title_full_unstemmed Finite element analysis of the vibration problem of a plate coupled with a fluid
title_sort finite element analysis of the vibration problem of a plate coupled with a fluid
publishDate 2000
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0029599X_v86_n4_p591_Duran
http://hdl.handle.net/20.500.12110/paper_0029599X_v86_n4_p591_Duran
work_keys_str_mv AT duranricardoguillermo finiteelementanalysisofthevibrationproblemofaplatecoupledwithafluid
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