Eigenderivative analysis of asymmetric non-conservative systems

In general, the damping matrix of a dynamic system or structure is such tha t it can not be simultaneously diagonalized with the mass and stiffness mat rices by any linear transformation. For this reason the eigenvalues and eig envectors and consequently their derivatives become complex. Expressions fo r the first- and second-order derivatives of the eigenvalues and eigenvecto rs of these linear, non-conservative systems are given. Traditional restric tions of symmetry and positive definiteness have not been imposed on the ma ss, damping and stiffness matrices. The results are derived in terms of the eigenvalues and left and right eigenvectors of the second-order system so that the undesirable use of the first-order representation of the equations of motion can be avoided. The usefulness of the derived expressions is dem onstrated by considering a non-proportionally damped two degree-of-freedom symmetric system, and a damped rigid rotor on flexible supports. Copyright (C) 2001 John Wiley & Sons, Ltd.