Modal Analysis of Elastic Vibrations of Incompressible Materials Based on a Variational Multiscale Finite Element Method

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

“…In this paper, our main objective is to present a modal analysis technique to simulate the linear elastic behavior of incompressible elastic solids where the incompressibility constraint is enforced by incorporating the pressure. The ultimate aim is to extend the robustness and effectiveness of the modal analysis in the mixed finite element framework recently proposed in [37]. In the system of transient elasticity equations consisting of a second order temporal derivative, a harmonic behavior of the displacement is assumed and each mode is considered to be of the form φ(x)e iωt , where φ(x) is the vector field of displacement amplitudes associated with the frequency ω.…”