Mohammadi, Seyyed AbbasSeyyed AbbasMohammadiVoß, HeinrichHeinrichVoß2019-06-262019-06-262018-10-01Mathematics and Mechanics of Solids 10 (23): 1377-1388 (2018-10-01)http://hdl.handle.net/11420/2828This paper proposes a new approach for computing the real eigenvalues of a multiple-degrees-of-freedom viscoelastic system in which we assume an exponentially decaying damping. The free-motion equations lead to a nonlinear eigenvalue problem. If the system matrices are symmetric, the eigenvalues allow for a variational characterization of maxmin type, and the eigenvalues and eigenvectors can be determined very efficiently by the safeguarded iteration, which converges quadratically and, for extreme eigenvalues, monotonically. Numerical methods demonstrate the performance and the reliability of the approach. The method succeeds where some current approaches, with restrictive physical assumptions, fail.en1081-286520181013771388Journal Article10.1177/1081286517726368Other