A dimensionally reduced order piezoelectric energy harvester model

Presently reduced power requirement for small electronic components have been the main motivation for developing vibration based energy harvesting. The ultimate objective in this research field is to provide an easy, sustainable and efficient technology to power such small electronic devices from the unused vibrational energy available in the environment. A comprehensive, reliable mathematical technique is thus in high demand which can model a piezoelectric energy harvester, predict its coupled dynamics (structural and electromechanical) accurately. The present work focuses on developing a mathematical model for a slender, piezoelectric energy harvester based on Variational Asymptotic Method, a dimensional reduction methodology. Variational Asymptotic Method approximates the 3D electromechanical enthalpy as an asymptotic series to formulate an equivalent 1D electromechanical enthalpy functional to perform a systematic dimensional reduction. For validation purpose, we have picked up experimental results for a bimorph PZT harvester, available in the literature. We have studied the extension-bending structural coupling along with the parameter dependence of the voltage, power output from the harvester and validated with the experiments. The present study provides a unique, accurate modeling technique which is capable of capturing material anisotropy, structural coupling and can analyse arbitrary cross section, surface mounted as well as embedded piezo layered energy harvester.