Dynamical response identification of a class of nonlinear hysteretic systems

The experimental dynamical response of three types of nonlinear hysteretic systems is identified employing phenomenological models togheter with the Differential Evolutionary algorithm. The mass–spring–damper system is characterized by hysteretic restoring forces provided by assemblies of shape memory and steel wire ropes subject to flexure or coupled states of tension and flexure. The energy dissipation due to phase transformations and inter-wire friction and the stretching-induced geometric nonlinearities give rise to different shapes of hysteresis cycles. The mechanical device subject to strong seismic excitations is investigated in its ultimate limit state whereby inelastic strains are induced in the steel wires together with a global nonsymmetric response of the system. The targeted dynamical characterization of the hysteretic oscillator up to its ultimate limit state has a special meaning when the device is employed in the field of vibration control. The dynamical response is identified exploiting the measurements of the oscillating mass relative displacement and inertia force that must be balanced, at each time instant, by the overall restoring forces provided by the mechanism. The restoring force is assumed to be the sum of different contributions such as a cubic nonsymmetric elastic force and a nonsymmetric hysteretic force modeled according to a modified version of the Bouc–Wen model. The parameters are identified minimizing the difference between the numerical and the experimental restoring force histories. High levels of accuracy are achieved in the identification with mean square errors lower than 2%.