Finite element analysis of the vibration problem of a plate coupled with a fluid
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...
Guardado en:
Autores principales: | , , , , |
---|---|
Formato: | JOUR |
Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0029599X_v86_n4_p591_Duran |
Aporte de: |
id |
todo:paper_0029599X_v86_n4_p591_Duran |
---|---|
record_format |
dspace |
spelling |
todo:paper_0029599X_v86_n4_p591_Duran2023-10-03T14:39:29Z Finite element analysis of the vibration problem of a plate coupled with a fluid Durán, R.G. Hervella-Nieto, L. Liberman, E. Rodríguez, R. Solomin, J. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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. |
format |
JOUR |
author |
Durán, R.G. Hervella-Nieto, L. Liberman, E. Rodríguez, R. Solomin, J. |
spellingShingle |
Durán, R.G. Hervella-Nieto, L. Liberman, E. Rodríguez, R. Solomin, J. Finite element analysis of the vibration problem of a plate coupled with a fluid |
author_facet |
Durán, R.G. Hervella-Nieto, L. Liberman, E. Rodríguez, R. Solomin, J. |
author_sort |
Durán, R.G. |
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 |
url |
http://hdl.handle.net/20.500.12110/paper_0029599X_v86_n4_p591_Duran |
work_keys_str_mv |
AT duranrg finiteelementanalysisofthevibrationproblemofaplatecoupledwithafluid AT hervellanietol finiteelementanalysisofthevibrationproblemofaplatecoupledwithafluid AT libermane finiteelementanalysisofthevibrationproblemofaplatecoupledwithafluid AT rodriguezr finiteelementanalysisofthevibrationproblemofaplatecoupledwithafluid AT solominj finiteelementanalysisofthevibrationproblemofaplatecoupledwithafluid |
_version_ |
1782025871757934592 |