A subspace iteration algorithm for the eigensolution of large structures subject to non-classical viscous damping

This paper describes an e cient and numerically stable algorithm for accurately computing the solutions of the quadratic eigenproblem associated to non-proportionally viscously damped structures characterized by symmetric matrices. Combining the simultaneous inverse iteration with a generalized Rayleigh{Ritz analysis, the proposed procedure is well suited for extracting the subset of the lowest natural frequencies, the corresponding subcritical damping ratios and the mode shapes of large dissipative systems with non-classical viscous damping. The iterative process exploits the speci c nature of non-proportionally damped structures, takes full advantage of the banded con guration of the structural matrices involved in the eigenproblem, avoids the computation of the left eigenvectors and circumvents the use of complex algebra owing to a unitary transformation strategy. An academic test case and an industrial numerical example are presented to highlight the e ectiveness of the algorithm.