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

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.R. Codina gratefully acknowledges the support received through the ICREA Academia Research Program of the Catalan Government, Spain. CIMNE is a recipient of a “Severo Ochoa Programme for Centres of Excellence in R&D” (grant CEX2018-000797-S) by the Spanish Government .Peer ReviewedPostprint (author's final draft