On the Use of Wavelet Transform to Characterize Chaotic Behavior of an Impact Oscillator

The Wavelet transform gives a 2D-space time-frequency presentation for responses in the 1Dspace time domain. This paper presents the results of investigating the application of wavelet transform to characterize the nonlinear and chaotic response of a clearance-coupled-impact system. The behavior of impacting systems is highly nonlinear exhibiting a myriad of harmonic, low order and high order sub-harmonic resonances, as well as chaotic vibrations. The timehistory simulations of the single-degree-of-freedom impact oscillator were obtained by the Neumark-β numerical integration algorithm. The accuracy of the results from the wavelet analysis were confirmed by comparing them with Poincare’ maps, fractal dimension, and Lyapunov exponents of the time domain response. The results are illustrated by graphs, which gives valuable insights on the dynamics of the impact system.