Generation of energy in console piezoelectric energy harvesters

Abstract

Energy harvesting of mechanical vibrations and their conversion into electrical energy using piezoelectric devices has become widespread. This has been made possible by the creation of high-energy piezoelectric materials and the proliferation of miniature devices with a few milliwatts of power.
 In this work, the oscillations of the rod cantilever bimorph energy harvester under harmonic loads are investigated. A two-layer rod consisting of a brass base and a rectangular piezoelectric element with electroded flat surfaces without and with tip mass is considered. The thickness of the layers is much less than the width and the width is much less than the length, which allows us to use the hypothesis of flat sections and assumptions of the potential difference linearity by thickness of the element, as well as beams bending relations.
 There is derived the characteristic equation for beam bending oscillations, the wave numbers, circular frequencies and natural frequencies are determined. There is carried out The averaging of material characteristics over the cross-sectional area. Eigenforms of oscillations are constructed, the dependence of natural frequencies from body size and tip mass is analyzed.
 The next step is to study the forced oscillations of the energy harvesters with tip mass at the end at given oscillations of the base. The equation of the elastic line of the console is formed, the maximum deflections and angles of rotation are determined. The voltage generated on the piezo element plates is determined taking into account the electrical resistance. Due to the voltage and resistance of the conduct line the power of the energy harvester is determined. Curves of voltage and power dependence from load frequency and external resistance are constructed. It is established that the voltage and power of the element change in proportion to R. The maximum power of the energy collector occurs in the vicinity of resonances, and before the first resonance the power is almost zero. Between the first and second resonance, the power is approximately 1,5 mW. During the transition to the ultrasonic zone, the power of the energy collector increases significantly.Analysis of the harvester operation at resonant frequencies requires consideration of the damping of oscillations in the material.