# Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements

- Volume: 38, Issue: 6, page 1055-1070
- ISSN: 0764-583X

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topHernández, Erwin. "Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.6 (2004): 1055-1070. <http://eudml.org/doc/244928>.

@article{Hernández2004,

abstract = {We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling is used on the fluid-structure interface. Applying a general approximation theory for spectral problems, under mild assumptions, we obtain optimal order error estimates for the computed eigenfunctions, as well as a double order for the eigenvalues. These estimates are valid with constants independent of the plate thickness. Finally, we report several numerical experiments showing the behavior of the methods.},

author = {Hernández, Erwin},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Reissner-Mindlin; MITC methods; fluid-structure interaction},

language = {eng},

number = {6},

pages = {1055-1070},

publisher = {EDP-Sciences},

title = {Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements},

url = {http://eudml.org/doc/244928},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Hernández, Erwin

TI - Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 6

SP - 1055

EP - 1070

AB - We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling is used on the fluid-structure interface. Applying a general approximation theory for spectral problems, under mild assumptions, we obtain optimal order error estimates for the computed eigenfunctions, as well as a double order for the eigenvalues. These estimates are valid with constants independent of the plate thickness. Finally, we report several numerical experiments showing the behavior of the methods.

LA - eng

KW - Reissner-Mindlin; MITC methods; fluid-structure interaction

UR - http://eudml.org/doc/244928

ER -

## References

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