Finite element analysis of the vibration problem of a plate coupled with a fluid |
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Authors: | RG Durán L Hervella-Nieto E Liberman R Rodríguez and J Solomin |
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Institution: | (1) Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina , AR;(2) Departamento de Matemática, Facultade de Informática, Universidade da Coru?a, 15071 - A Coru?a, Spain , ES;(3) Comisión de Investigaciones Científicas de la Provincia de Buenos Aires and Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 172., 1900 – La Plata, Argentina , AR;(4) Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile , CL;(5) Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 172., 1900 - La Plata, Argentina , AR |
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Abstract: | Summary. 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 , and introduce appropriate scalings for the physical parameters so that these problems attain a limit when . 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. Finally we present numerical results confirming the good performance of the method.
Received February 4, 1998 / Revised version received May 26, 1999 / Published online June 21, 2000 |
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Keywords: | Mathematics Subject Classification (1991): 65N30 65N25 |
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