# Finite element analysis of sloshing and hydroelastic vibrations under gravity

Alfredo Bermúdez; Rodolfo Rodríguez

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 2, page 305-327
- ISSN: 0764-583X

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topBermúdez, Alfredo, and Rodríguez, Rodolfo. "Finite element analysis of sloshing and hydroelastic vibrations under gravity." ESAIM: Mathematical Modelling and Numerical Analysis 33.2 (2010): 305-327. <http://eudml.org/doc/197598>.

@article{Bermúdez2010,

abstract = {
This paper deals with a finite element method to solve fluid-structure
interaction problems.
More precisely it concerns the numerical computation of harmonic
hydroelastic vibrations under gravity.
It is based on a displacement formulation for both the fluid and the solid.
Gravity effects are included on the free surface of the fluid as well
as on the liquid-solid interface.
The pressure of the fluid is used as a variable for the theoretical
analysis leading to a well posed mixed linear eigenvalue problem.
Lowest order triangular Raviart-Thomas elements are used for the
fluid and classical piecewise linear elements for the solid.
Transmission conditions at the fluid-solid interface are taken into
account in a weak sense yielding a non conforming discretization.
The method does not present spurious or circulation modes for
nonzero frequencies.
Convergence is proved and optimal error estimates are given.
Finally, numerical results are shown.
},

author = {Bermúdez, Alfredo, Rodríguez, Rodolfo},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Fluid-structure; finite elements; hydroelasticity under gravity;
vibrations; spectral problems; spurious modes.; gravity effects; spurious modes; finite element method; fluid-structure interaction problems; harmonic hydroelastic vibrations; displacement formulation; well-posed mixed linear eigenvalue problem; triangular Raviart-Thomas elements; piecewise linear elements; fluid-solid interface; non-conforming discretization; convergence; optimal error estimates},

language = {eng},

month = {3},

number = {2},

pages = {305-327},

publisher = {EDP Sciences},

title = {Finite element analysis of sloshing and hydroelastic vibrations under gravity},

url = {http://eudml.org/doc/197598},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Bermúdez, Alfredo

AU - Rodríguez, Rodolfo

TI - Finite element analysis of sloshing and hydroelastic vibrations under gravity

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 2

SP - 305

EP - 327

AB -
This paper deals with a finite element method to solve fluid-structure
interaction problems.
More precisely it concerns the numerical computation of harmonic
hydroelastic vibrations under gravity.
It is based on a displacement formulation for both the fluid and the solid.
Gravity effects are included on the free surface of the fluid as well
as on the liquid-solid interface.
The pressure of the fluid is used as a variable for the theoretical
analysis leading to a well posed mixed linear eigenvalue problem.
Lowest order triangular Raviart-Thomas elements are used for the
fluid and classical piecewise linear elements for the solid.
Transmission conditions at the fluid-solid interface are taken into
account in a weak sense yielding a non conforming discretization.
The method does not present spurious or circulation modes for
nonzero frequencies.
Convergence is proved and optimal error estimates are given.
Finally, numerical results are shown.

LA - eng

KW - Fluid-structure; finite elements; hydroelasticity under gravity;
vibrations; spectral problems; spurious modes.; gravity effects; spurious modes; finite element method; fluid-structure interaction problems; harmonic hydroelastic vibrations; displacement formulation; well-posed mixed linear eigenvalue problem; triangular Raviart-Thomas elements; piecewise linear elements; fluid-solid interface; non-conforming discretization; convergence; optimal error estimates

UR - http://eudml.org/doc/197598

ER -

## Citations in EuDML Documents

top- Mauricio A. Barrientos, Gabriel N. Gatica, Rodolfo Rodríguez, Marcela E. Torrejón, Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem
- Mauricio A. Barrientos, Gabriel N. Gatica, Rodolfo Rodríguez, Marcela E. Torrejón, Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem

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