Identification of Damping: Part 3, Symmetry-preserving Methods

In two recent papers (Adhikari and Woodhouse 2001 Journal of Sound and <ibration 243, 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 identi"ed 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 identi"ed 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. 2002 Elsevier Science Ltd.