On the relationship between viscous and hysteretic damping models and the importance of correct interpretation for system identification

In engineering practice, both viscous and hysteretic damping models are usually employed to characterize damped dynamic properties of linear mechanical systems, the identification of which has long been an active area of research in experimental modal analysis. This paper is devoted to investigate the relationship between viscous and hysteretic damping models. In order to show whether the arbitrary choice of damping model is reasonable, the relationship has been derived based on two normalization procedures and the modal parameter identification procedure. In case of proportional damping, there exists an exact relationship between hysteretic and viscous damping models as η r = 2 ξ r . As for non-proportional damping, the equivalent mode shapes and their counterparts of the original system are almost the same except differing by a complex scaling factor. The numerical cases based on the simulated modal identification procedure have demonstrated that the error in the estimation of modal parameters caused by arbitrarily choosing damping model is quite small. Furthermore, the equivalent damping matrix is physically sensible in the case of the system with distributed damping whereas, no physically sensible equivalent damping matrix exists in the case where the damping is localized. The validity of the relationship between the two damping models has been further verified by a practical experimental example.