Identification of Non-linear Vibrating Systems based on Instantaneous Frequencies and Amplitudes of Dynamic Response

Many physical phenomena that are observed cannot be described by a linear relationship. Actually, nonlinearity is generic in nature, and linear behavior is an exception. Nonlinearity may arise from geometrical nonlinearities (i.e. large deformation), material nonlinearities (i.e. elastoplastic material), and contact. So characterization of the nonlinear behavior may provide critical diagnostic and prognostic information. At present, one may analyze structures using tools with assumptions of linear and stationary behavior. Determination of Dynamic characteristics assuming linearity and stationarity for a structure, while exhibits nonlinear behavior, can lead to highly misleading results. Hence, it is essential to know whether a structure behaves nonlinearly or one can able to detect and estimate nonlinearity effects both qualitatively and quantitatively. This is where time-frequency domain analysis can be applied as an appropriate diagnostic tool. It is possible that the instantaneous frequencies and amplitudes of the dynamic response of a nonlinear structure, which may be obtained by wavelet analysis, be used to characterize and identify the nonlinear behavior of the structure. In the present paper will be shown that even in the presence of noise the instantaneous characteristics derived from wavelet analysis can be considered as a suitable benchmark for estimating parameters of the nonlinear system. To validate what has been proposed, inverse identification of a nonlinear Duffing system is carried out. In this path, to achieve proper resolution in wavelet analysis in both time and frequency domains, the best shape of the wavelet function is obtained by minimizing the conditional entropy.