A state-space methodology to identify modal and physical parameters of non-viscously damped systems

In this paper, a new methodology is proposed to identify modal and physical parameters of linear non-viscously damped multi-degree-of-freedom systems using recorded time-histories of their dynamic response. The methodology is based on the identification of a symmetric state-space realization of the system, whose modal parameters (spectral and modal matrices) are subsequently used to determine the physical parameters (mass, stiffness and damping matrices) of the model in second-order form. The state-space formulation, well known in the literature for systems with viscous damping, is extended to systems with non-viscous damping through the use of additional internal variables, devoted to represent the dependence of the dissipative forces on the past history of generalized velocities. The methodology is validated by means of numerical simulations aiming at assessing its accuracy and the errors possibly due to incomplete experimental data. Considering that the general non-viscous model is able to represent also the viscous damping behaviour as a special case of memmyless damping, applications are eventually provided to investigate the applicability of the proposed methodology to the identification of both proportional and non-proportional viscously damped systems