Analysis and Optimal Design of Vibration-Based Paddle Type Piezoelectric Energy Harvester Under Electrostatic Actuation

Purpose: This study aims to model the energy harvesting from bending vibrations of a cantilever paddle beam with a piezoelectric layer under electrostatic excitation. Electrostatic excitation is induced by a layer of electrons placed against the paddle surface. When the paddle surface is charged, an electrostatic force is applied to the paddle surface. It causes the cantilever paddle beam to be pulled towards the opposite electrode plate. When the paddle hits the electrode, it is discharged and the beam is released. Methods: Differential equations governing free vibrations of the system are first derived using Hamilton’s principle. Then, the natural frequency and free vibration mode shapes of the system are obtained by separating variables method. The forced vibration equation coupled with the equations governing the output voltage of the piezoelectric layer are derived using assumed modes method. Gauss’s law is used to obtain the electromechanical equations governing the piezoelectric layer. The resulting equations are solved by Runge–Kutta numerical method. Finally, using the optimization algorithm based on the Runge–Kutta numerical method, the optimal non-prismatic shape of the piezoelectric layer and other design variables related to piezoelectric layer are calculated. Results and Conclusions: The results indicate that width, length, thickness, and mass of paddle surface and also its distance from opposite electrode could significantly affect the amount of energy harvested in a specific time period. The results demonstrate that the average energy harvested in the optimal design mode has increased by seven times compared to the classical model.