Analysis of an energy harvesting piezoelectric beam with energy storage circuit

Accurate (distributed-parameter) models of energy harvesting piezoelectric beams have recently been presented and experimentally validated. However, these studies were limited in their practical significance since the external electrical load was assumed to be a simple linear impedance (resistor or capacitor), without any means of energy storage. This paper presents and validates experimentally a mathematical model of a base-excited piezoelectric cantilever connected across an energy storage circuit comprising a diode in series with a capacitor. The resulting half-wave AC-DC rectification enables the capacitor to retain a part of the harvested energy (i.e. accumulate a mean voltage). The Euler-Bernoulli beam model with piezoelectric coupling is used. The resulting wave equation is transformed into modal space using the analytical modal analysis method (AMAM). The Shockley diode equation is used to model the current. The resulting nonlinear system of equations is solved for a prescribed base motion input using a numerical integration routine. The analysis of the same cantilever connected across an unrectified capacitor is also performed for comparative purposes. Theoretical studies show that, for the case of the rectified capacitor, as well as the unrectified capacitor, the energy harvesting effect does not have a dampening effect on the steady-state vibration. However, whereas the resonance frequency of the unrectified system is a function of the load, the resonance frequency of the rectified system is fixed at a value that is very close to the open circuit resonance frequency of the unrectified system. The theoretical findings are validated by the experimental results.