Nonlinear system identification of a double-well Duffing oscillator with position-dependent friction

A double-well Duffing oscillator with nonlinear damping is identified in this paper, using the nonlinear subspace identification (NSI) technique in conjunction with a novel virtual input perturbation approach. This kind of system exhibits a negative stiffness characteristic, which has become popular in engineering applications such as vibration absorbers. The studied device exhibits strong nonlinear elastic and damping behaviors. In particular, the latter results in a very challenging identification, and the applicability of the proposed method to nonlinear damping is therefore discussed. In this context, the method is first tested considering simulations with quadratic friction. The experimental investigation is eventually undertaken considering a broadband random excitation, with a friction model depending on both velocity and displacement. Results show that NSI is capable of estimating the nonlinear model associated with stiffness and damping nonlinearities with a high level of confidence. This is particularly true in the case of complex nonlinear behaviors related to the double-well characteristics, using the proposed virtual input perturbation technique. This is confirmed also by the proposed experimental application and enlarges the range of applications of the NSI technique.