Diagonalization methods for viscous and hysteretic damping matrices

A method to obtain damping matrices which are diagonalized by the undamped eigenmodes and which are equivalent to the true viscous and hysteretic damping matrices is presented. The method is based on the assumption that the damped complex eigenmodes of a structure with non proportional damping can be expressed as a linear combination of the first few undamped modes. In addition a simplified procedure is presented which is based on perturbation techniques. This simplified procedure allows to evaluate straightforwardly an equivalent damping matrix when the damping is sufficiently low. A criterium is suggested to judge when this simplified procedure can be accepted. (orig.)