# Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method

2022-09-01
Codina, Ramon
Türk, Önder
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.
Finite Elements in Analysis and Design

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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. 