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Numerische Mathematik

, Volume 86, Issue 4, pp 591–616 | Cite as

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

  • R.G. Durán
  • L. Hervella-Nieto
  • E. Liberman
  • R. Rodríguez
  • J. Solomin
Original article

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 \(t>0\), and introduce appropriate scalings for the physical parameters so that these problems attain a limit when \(t\to 0\). 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. Finally we present numerical results confirming the good performance of the method.

Mathematics Subject Classification (1991): 65N30, 65N25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • R.G. Durán
    • 1
  • L. Hervella-Nieto
    • 2
  • E. Liberman
    • 3
  • R. Rodríguez
    • 4
  • J. Solomin
    • 5
  1. 1.Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina AR
  2. 2.Departamento de Matemática, Facultade de Informática, Universidade da Coruña, 15071 - A Coruña, Spain ES
  3. 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. 4.Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile CL
  5. 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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