IDENTIFICATION OF DAMPING: PART 3, SYMMETRY-PRESERVING METHODS

In two recent papers (Adhikari and Woodhouse 2001 Journal of Sound and Vibration243, 43–61; 63–88), methods were proposed to identify viscous and non-viscous damping models for vibrating systems using measured complex frequencies and mode shapes. In many cases, the identified damping matrix becomes asymmetric, a non-physical result. Methods are presented here to identify damping models which preserve symmetry of the system. Both viscous and non-viscous models are considered. The procedure is based on a constrained error minimization approach and uses only experimentally identified complex modes and complex natural frequencies together with, for the non-viscous model, the mass matrix of the system. The methods are illustrated by numerical examples.