Transient responses of non-proportionally damped structures by the group theoretic approach

Large scale dynamic finite element analysis of structural systems can be very expensive. To significantly reduce the computational cost various techniques have been developed and presented in the literature. The reduction method based on symmetry group or the so-called group theoretic approach (CTA) has been demonstrated to be a superior means for the bifurcation analysis and free vibration analysis of geometrically nonlinear systems with symmetries by Healey and associates, and others. This method has recently been extended by the authors to deal with large geometrically nonlinear static and dynamic responses of structures discretized by the finite element method. The present paper is, however, concerned with the introduction and application of the extended GTA to systems with non-proportional damping without recourse to the complex modal analysis. It is shown that the extended GTA is simple, efficient and accurate. Consequently, it can prove to be a powerful and economical method to be employed for the computation of accurate transient responses of large scale structural systems with or without non-proportional damping.