Identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform

We consider the free response of a nonlinear vibrating system. Using the ridges and skeletons of the continuous wavelet transform, we identify weak nonlinearities on damping and stiffness and estimate their physical parameters. The crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform. The method is applied to simulated single-degree-of-freedom systems and multi-degree-of-freedom systems with nonlinearities on damping and stiffness. Experimental validation of the nonlinear identification and parameter estimation method is presented. The experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor.