Understanding Effects of Tapering Cantilevered Piezoelectric Bimorphs for Energy Harvesting from Vibrations

Abstract

Piezoelectric energy harvesting from vibrations is a field that has gathered much attention over the past decade. The purpose of this application is to realize ambient sources of kinetic energy such as vibrations, and turn them into useful electrical energy for powering low powered sensor nodes. The most typical form of piezoelectric energy harvesting comes from cantilevered bimorphs. These bimorph structures are typically rectangular in shape with a tip mass, resonating in the fundamental mode of vibration. This creates a stress concentration near the fixed end of the cantilever, which linearly decreases towards the free end, hence creating an inefficient system. In order to improve this scenario by achieving a constant axial strain profile through the length of the geometry, tapered cantilevered bimorphs have been proposed in literature. However, an exhaustive set of experimental data and proper characterization, with appropriate constraints such as matching resonance frequency to prove this concept is elusive. In this dissertation, the effect of changing the geometry from rectangular cantilevered bimorphs into triangular ones with matching resonance frequency and volumes is presented. It is shown that for tapered geometry with matching volume and resonance frequencies, triangular bimorphs operate at lower maximum stresses, and provide enhanced electromechanical coupling coefficients. With enhanced electromechanical coupling coefficients, the impedance at resonance is lower, providing a smaller optimal load resistance value from which power can be extracted at lower currents. The absolute values of peak capacitance are also enhanced, with larger positive capacitance peaks and smaller negative capacitance peaks for triangular cantilevers as compared to rectangular counterparts. Studies for damping ratios as a function of load resistance also show damping ratios at optimal load resistance values indicate optimal damping ratios for power generation exist for high coupling systems. With increased electromechanical coupling and damping, triangular bimorphs provide higher electromechanical coupling figure of merits, when they can be compared with matching size, proof mass, and frequencies.