A Comparison of time-frequency methods for nonlinear dynamics and chaos analysis of the portal frame model as an energy harvester

Abstract

In this paper, we propose a study of an energy harvesting model based on a portal frame structure with non-ideal force of excitation. The non-ideal force is a DC motor with an unbalanced mass. The piezoelectric coupling was modeled to exhibit non-linear characteristics. This analysis was carried out through nu- merical simulation means of the mathematical formulation proposed. Thus, it plotted a Bifurcation Diagram to investigate the dynamic behavior by varying the voltage applied to the DC motor. A Poincare Section and Lyapunov Exponents were used to check the dynamic behavior for two different responses. The power harvesting was analyzed for two different dynamic response: periodic and chaotic behavior. Furthermore, the system was analyzed with Continuous Wavelet Trans- form, Synchrosqueezed Wavelet Transform and Instantaneous Frequency by Hil- bert Transform. This allows the examination of the signal in the time-frequency domain and analyzes the dynamic behavior and power harvesting.