The Use of Wavelets Analysis to Characterize the Dynamic Behavior of Energy Transfer Vibrational Systems

This paper describes the use of wavelet analysis for identification of regular and irregular behavior of dynamical systems. We are focused in single and double-well potential energy harvesting systems that present either periodic or chaotic behavior. To identify the behavior of dynamical systems is of major importance in predicting possible energy harvesting from that system. Using Morlet wavelets, the oscillatory motions of a set of systems were identified with good accuracy. The visualization of the scalograms and global energy spectrum are very useful tools to validate the type of motion found, periodic, quasi-periodic or chaotic. Wavelet analysis can be used to find which amplitude and frequency of operation that generates more energy for each model. Wavelet analysis is a technique used as a tool to assist the validation of the presence of chaos in dynamic systems, together with well consolidated techniques as Lyapunov exponents and Poincare maps.