Resistive and reactive loads' influences on highly coupled piezoelectric generators for wideband vibrations energy harvesting

One of the main challenges in energy harvesting from ambient vibrations is to find efficient ways to scavenge the energy, not only at the mechanical system resonance but also on a wider frequency band. Instead of tuning the mechanical part of the system, as usually proposed in the state of the art, this article develops extensively the possibility to tune the properties of the harvester using the electrical interface. Due to the progress in materials, piezoelectric harvesters can exhibit relatively high electromechanical coupling: hence, the electrical part can now have a substantial influence on the global parameters of the piezoelectric system. In order to harness the energy efficiently from this kind of generator on a wide frequency band, not only the electrical load's effect on the harvester's damping should be tuned but also its effect on the harvester's stiffness. In this article, we present an analytical analysis of the influences of the resistive and reactive behavior of the electrical interface on highly coupled piezoelectric harvesters. We develop a normalized study of the multiphysics interactions, reducing the number of parameters of the problem to a few physically meaningful variables. The respective influence of each of these variables on the harvesting power has been studied and led us to the optimal electrical damping expression and the influences of the damping and of the coupling on the equivalent admittance of the piezoelectric energy harvester. Finally, we linked these normalized variables with real reactive load expressions, in order to study how a resistive, capacitive, and inductive behavior could affect the global performances of the system. The theoretical analysis and results are supported by experimental tests on a highly coupled piezoelectric system (k2=23%). Using an adequate tuning of a RC load at each frequency, the maximum harvested power (11 mu W) under a small acceleration amplitude of 0.5ms-2 is reached over a 14 Hz large frequency band around 105 Hz which has been predicted by the model with less than 5% error.