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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Citation Formats

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.