A Comparison of Time-Frequency Methods for Nonlinear Dynamics and Chaos Analysis in an Energy Harvesting Model

In this paper, an energy harvesting model based on a portal frame structure, modeled as a duffing system, with a non-ideal excitation force, DC motor with an unbalanced mass, is presented and the piezoelectric coupling is designed to exhibit nonlinear characteristics. Nonlinearity included provides higher power output over a wide frequency range. This analysis was carried out by numerical simulation of the proposed mathematical formulation. Thus, the bifurcation diagram and the largest Lyapunov exponents are plotted to investigate the dynamic behavior by ranging the voltage applied to the DC motor. In this way, power harvesting is analyzed for two different dynamic responses: periodic and chaotic behavior. Furthermore, this work exhibits an application of frequency-domain techniques, such as short-time Fourier transform, continuous wavelet transform, synchrosqueezed wavelet transform, and Wigner-Ville distribution methods. These methods are often used to analyze non-stationary signals, allowing the verification of dynamic behavior and power harvesting. Therefore, this paper aims to apply the time-frequency methods, mentioned previously, to analyze the mechanical system response in different behaviors.