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Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method
Date
2022-09-01
Author
Codina, Ramon
Türk, Önder
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This paper describes a modal analysis technique to approximate the vibrations of incompressible elastic solids using a stabilized finite element method to approximate the associated eigenvalue problem. It is explained why residual based formulations are not appropriate in this case, and a formulation involving only the pressure gradient is employed. The effect of the stabilization term compared to a Galerkin approach is detailed, both in the derivation of the approximate formulation and in the error estimate provided.
Subject Keywords
Eigenvalue problems
,
Incompressible elastic waves
,
Modal analysis
,
Stabilized finite element methods
URI
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85127493371&origin=inward
https://hdl.handle.net/11511/96833
Journal
Finite Elements in Analysis and Design
DOI
https://doi.org/10.1016/j.finel.2022.103760
Collections
Graduate School of Applied Mathematics, Article
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R. Codina and Ö. Türk, “Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method,”
Finite Elements in Analysis and Design
, vol. 206, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85127493371&origin=inward.