turkmath.org

Modal analysis is a typical approach employed to approximate vibration problems of elastic materials. The key idea is to assume a harmonic behaviour for the displacement utilizing the second order time derivatives in the inertia term, and thus to transform the problem into an eigenvalue problem. The set of equations is form identical to the Stokes equations which govern the incompressible creeping flow of viscous fluids, and is a constituent of Navier-Stokes equations. In this talk, will concentrate on a stabilized finite element  method formulated in a variational multiscale framework where the continuous space is approximated by a direct sum of the finite element space and its orthogonal complement. We shall show that the numerical procedure provides a reasonably realistic description of the eigenspectrum of the associated operator affirming that there are no spurious eigenvalues. Once the eigenspace has been built, the time approximation to the solution of the continuous problem is obtained making use of a few modes of the whole set, those with higher energy. The presentation will include several theoretical and numerical results from joint works with Daniele Boffi and Ramon Codina.

Link to the Seminar is :

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1603456597648?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d