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.

► We consider the damping matrix depending on frequency and on a set damping parameters. ► The eigensolutions are multi-variable functions of these parameters. ► Eigenvalues are approximated as solutions of certain ordinary differential equation. ► Method is available for proportional and for non-proportional damping MDOF systems. ► Accuracy depends on the level of induced damping.