Eigenvalue and eigenvector computation for discrete and continuous structures composed of viscoelastic materials

Both discrete and continuous structures, with frequency and/or temperature dependent viscoelastic elements, gives rise to a nonlinear eigenvalue problem. An accurate computation of eigenvalues (natural frequencies) and eigenvectors (mode shapes) is essential for control, design sensitivities, and optimization studies. In this paper, a pth order approximation of a general nonlinear eigenvalue problem is formulated. A numerical approach to simultaneously compute the eigenvalues and associated left and right eigenvectors is presented. This method can be used for both discrete and continuous systems with viscoelastic elements. Numerical examples are presented here to demonstrate its effectiveness and for the validation purposes.