Multiparametric computation of eigenvalues for linear viscoelastic structures

A new methodology for the computation of complex eigenvalues for multi-degree-of-freedom linear viscoelastic structures is presented. It is assumed that damping matrix does not only depends on the frequency but also on a set of parameters that control the dissipative mechanisms. Eigenvalues are then functions of a multi-variable array formed by damping parameters. The key idea is to approximate the eigenvalues as solutions of a specially developed differential equation. Proportional and non-proportional damping are studied separately. In addition, the error order and the computational complexity are rigorously analyzed. Numerical examples show very good agreement between proposed and exact solutions.This research was partially supported by the Grants CSD2008-00037 Canfranc Underground Physics and Polytechnic University of Valencia under programs PAID 02-11-1828 and 05-10-2674.Lázaro, M.; Pérez-Aparicio, JL. (2013). Multiparametric computation of eigenvalues for linear viscoelastic structures. Computers and Structures. 117:67-81. https://doi.org/10.1016/j.compstruc.2012.12.003678111