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


Codina R., TÜRK Ö.

Finite Elements in Analysis and Design, vol.206, 2022 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 206
  • Publication Date: 2022
  • Doi Number: 10.1016/j.finel.2022.103760
  • Title of Journal : Finite Elements in Analysis and Design
  • Keywords: Eigenvalue problems, Incompressible elastic waves, Modal analysis, Stabilized finite element methods

Abstract

© 2022 Elsevier B.V.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.