Rates of Change of Eigenvalues and Eigenvectors in Damped Dynamic System

Rates of change of eigenvalues and eigenvectors of a damped linear discrete dynamic system with respect to the system parameters are presented. A non-proportional viscous damping model is assumed. Due to the non-proportional nature of the damping the mode shapes and natural frequencies become complex, and as a consequence the sensitivities of eigenvalues and eigenvectors are also complex. The results are presented in terms of the complex modes and frequencies of the second order system and the use of rather undesirable state-space representation is avoided. The usefulness of the derived expressions is demonstrated by considering an example of a non-proportionally damped two degree-of-freedom system.