Modeling of a Porous Piezoelectric Nano Energy Harvester Based on Timoshenko-Beam Theory

Collecting electric power from the vibration of piezoelectric beams is practical and has been widely used for decades. This paper investigates a porous piezoelectric cantilever Timoshenko-beam energy harvester at nanoscale. The aim is to propose an optimized Timoshenko beam in order to gain more power with the same working conditions. For this purpose, the width of the beam is assumed to be exponentially changing and pores are also introduced into the beam to relieve the inherent brittleness of piezoelectric materials. Based on Timoshenko beam theory and porous piezoelectric elasticity, the uncoupled motion equations of the porous piezoelectric nanoTimoshenko beam are deduced. The analytical solutions to the output voltage and power density are obtained. According to the numerical calculation, it can be concluded that the electrical output can be improved by increasing the section parameter. Moreover, the surface effects and pore properties on the energy harvesting characteristics are discussed. In addition, when there is a concentrated mass at the free end of the beam, the displacements and output power are studied.