Issues in mathematical modeling of piezoelectric energy harvesters

Abstract

The idea of vibration-to-electric energy conversion for powering small electroniccomponents by using the ambient vibration energy has been investigated by researchersfrom different disciplines in the last decade. Among the possible transduction mechanisms,piezoelectric transduction has received the most attention for converting ambient vibrationsto useful electrical energy. In the last five years, there have been a considerable number ofpublications using various models for the electromechanical behavior of piezoelectricenergy harvester beams. The models used in the literature range from elementarysingle-degree-of-freedom (SDOF) models to approximate distributed parameter models aswell as analytical distributed parameter solution attempts. Because of the diverse nature ofresearchers working in energy harvesting (including electrical, mechanical and materialsengineers), several oversimplified and incorrect physical assumptions have been propagatedin the literature. Issues of the correct formulation for piezoelectric coupling, correctphysical modeling, use of low fidelity models, incorrect base motion modeling, andthe use of static expressions in a fundamentally dynamic problem are discussedand clarified here. These common indiscretions, which have been repeated in theexisting piezoelectric energy harvesting literature, are addressed and clarifiedwith improved models, and examples are provided. This paper aims to providecorrections and necessary clarifications for researchers from different engineeringdisciplines interested in electromechanical modeling of piezoelectric energy harvesters.