Nonlinear Interaction, Bifurcation, and Energy Harvesting in a Coupled Two-Degree-of-Freedom Mechanical System with a Piezoelectric RC-Circuit

The dynamics of a master-slave system connected to a piezoelectric (PZ) energy harvester are examined in this paper. The complete system is mathematically represented as a two-degree-of-freedom (2-DOF) scheme, linked to a first-order differential equation governing the extraction of electrical voltage during harvesting. According to the claim of the perturbation method, the equations governing the modulation of oscillation amplitudes, known as slow flow modulating equations, are derived. Subsequently, the impact of various system parameters on both vibration amplitudes and harvesting voltage is investigated by inspecting different response curves. The results demonstrate that the system under consideration can exhibit periodic or quasi-periodic movement subject to the chosen system parameters. Based on these analytical investigations, optimal system parameters for energy harvesting (EV) and vibration control purposes are determined. Furthermore, numerical simulations are achieved to confirm the analytical results. The simulations employ time response, phase plane, Poincare map, and bifurcation diagram analyses, which confirm the excellent agreement between the numerical and analytical results obtained.