Alternating Frequency Time Domains identification technique: Parameters determination for nonlinear system from measured transmissibility data

In order to better understand nonlinearity, a substantial number of methods have been devoted to extract the stiffness and damping functions. Although most identification methods are based on mathematical models, some promising methods rely mainly on the use of non-parametric techniques, by plotting and adjusting the restoring force to displacement and velocity in the time or frequency domains. However, the identification process in these methods is limited to amplitude-dependence and the identification of nonlinearities that depend on both frequency and amplitude is still required. This is the reason why, in this paper, a nonparametric identification procedure is proposed and an amplitude-frequency-dependent model is developed to predict the system's dynamic behavior under different working conditions. The proposed approach is demonstrated and validated through number of numerical examples with nonlinearities, typically encountered in common engineering applications. Thereafter, this approach is implemented to determine the unknown parameters of a metal mesh isolator from transmissibility data. An application of this technique for identifying the nonlinearity of SDOF system subjected to multi-harmonic excitation is also illustrated.