A nonlinear eigenmode solver for linear viscoelastic structures

Abstract

This article deals with the nonlinear eigenvalue problem originating from the finite element discretization of mechanical structures involving linear viscoelastic material. The material function is assumed to be positive real, which allows a location of the eigenvalues in the left complex half space of the Laplace domain. The solution method for the considered nonlinear eigenvalue problem is based on the contour integral method, where special focus is put on the efficient numerical computation of the linear system along the boundary of the given search area. For this purpose, the reduced order model technique is used and appropriate a priori error estimates are provided. Finally, the validity of the proposed method is illustrated in numerical examples.