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Approximation of a structural acoustic vibration problem by hexahedral finite elements

Approximation of a structural acoustic vibration problem by hexahedral finite elements
Approximation of a structural acoustic vibration problem by hexahedral finite elements
A finite-element method to compute elastoacoustic vibration modes in 3D problems on hexahedral meshes is analysed. It is based on displacement formulations for solid and fluid domains. In order to avoid spurious modes, the discretization consists of lowest order hexahedral Raviart–Thomas elements for the former coupled with classical trilinear isoparametric hexahedral elements for the latter. The kinematic constraint is weakly imposed and the meshes on the fluid and solid domains do not need to match on the common interface. Basic interpolation results are proved for the lowest order hexahedral Raviart–Thomas elements. These results are used to prove convergence of the coupled finite-element method, non-existence of spurious modes and optimal-order error estimates for eigenfunctions and eigenvalues, under the assumption that the meshes on the fluid domain are asymptotically parallelepiped. Numerical results showing sufficiency and necessity of this hypothesis are reported.
structural acoustic vibrations, finite-element spectral approximation, hexahedral Raviart–Thomas elements
0272-4979
391-421
Bermudez, A.
27183172-1114-46d3-bbd9-141879027362
Gamallo, P.
4a10847b-5368-4f60-aab6-19a80b8556c9
Nogueiras, M.R.
14d36554-d1e9-4c49-8b6f-b5049cb20ac7
Rodriguez, R.
7ba4d3ae-a71a-4e93-af30-34592ca72163
Bermudez, A.
27183172-1114-46d3-bbd9-141879027362
Gamallo, P.
4a10847b-5368-4f60-aab6-19a80b8556c9
Nogueiras, M.R.
14d36554-d1e9-4c49-8b6f-b5049cb20ac7
Rodriguez, R.
7ba4d3ae-a71a-4e93-af30-34592ca72163

Bermudez, A., Gamallo, P., Nogueiras, M.R. and Rodriguez, R. (2006) Approximation of a structural acoustic vibration problem by hexahedral finite elements. IMA Journal of Numerical Analysis, 26 (2), 391-421. (doi:10.1093/imanum/dri032).

Record type: Article

Abstract

A finite-element method to compute elastoacoustic vibration modes in 3D problems on hexahedral meshes is analysed. It is based on displacement formulations for solid and fluid domains. In order to avoid spurious modes, the discretization consists of lowest order hexahedral Raviart–Thomas elements for the former coupled with classical trilinear isoparametric hexahedral elements for the latter. The kinematic constraint is weakly imposed and the meshes on the fluid and solid domains do not need to match on the common interface. Basic interpolation results are proved for the lowest order hexahedral Raviart–Thomas elements. These results are used to prove convergence of the coupled finite-element method, non-existence of spurious modes and optimal-order error estimates for eigenfunctions and eigenvalues, under the assumption that the meshes on the fluid domain are asymptotically parallelepiped. Numerical results showing sufficiency and necessity of this hypothesis are reported.

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More information

Published date: 2006
Keywords: structural acoustic vibrations, finite-element spectral approximation, hexahedral Raviart–Thomas elements

Identifiers

Local EPrints ID: 28375
URI: https://eprints.soton.ac.uk/id/eprint/28375
ISSN: 0272-4979
PURE UUID: 25011f42-e194-4d03-9918-a411a4fb35ff

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Date deposited: 02 May 2006
Last modified: 15 Jul 2019 19:10

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