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.