Computing eigenpairs of quadratic eigensystems

The main objective of this paper is to introduce an algorithm for solving dependent eigenproblems. The global matrices of these eigenproblems are formulated by using a mixed finite element approach. This approach uses both the polynomial and frequency dependent displacement fields.The algorithm that is introduced is based on solving a sequence of linear eigenproblems by an appropriate eigensolver and updating the parameter by a safeguarded zerofinder.The eigensolution technique that has been developed is designed to evaluate a specific set of parameterized eigenvalues. Numerical experiments show that this eigentechnique accurately evaluates the first ten eigenvalues of quadratic eigenproblems.