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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 38.6 (2010): 1055-1070. <http://eudml.org/doc/194247>.

@article{Hernández2010,

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},

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

language = {eng},

month = {3},

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/194247},

volume = {38},

year = {2010},

}

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

DA - 2010/3//

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/194247

ER -

## References

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