Energy Harvesting and Nonlinear Dynamics of a Two-Degree of Freedom Master-Slave System Integrated with a Piezoelectric Actuator

This study explores the dynamics of a piezoelectric energy harvester coupled with a master-slave system. The entire system is modeled as a two-degree-of-freedom system (2-DOF), along with a first-order differential equation governing the dynamics of the harvested voltage. The perturbation method is applied to derive the slow-flow modulating equations that govern the master-slave oscillation amplitudes and phases. By analyzing various response curves, the effects of different system parameters on both vibration amplitudes and harvesting voltage are investigated. The findings indicate that the system can be controlled as a vibration control or energy harvester. Optimal parameters for energy harvesting as well as for vibration control purposes are reported based on analytical investigations. The results are validated through numerical simulations with MATLAB algorithms (ODE45) using time response, phase plane, Poincaré map, and bifurcation diagram, where an excellent agreement between the numerical solutions with matlap and analytical investigations with multiple time scales method has been demonstrated.