Effect of Hysteresis on a Piezoelectric Inverted Beam Energy Harvester

Abstract

Abstract Piezoelectric materials have been used in various types of structures to harvest ambient vibration energy by converting mechanical deformation to electrical charge. The harvested power can be used to charge batteries and/or operate low-power electronics such as wireless sensors. So-called linear piezoelectric devices can harvest vibrational energy efficiently only around the resonant frequency of the device. Ambient vibrations are typically multi-tone excitations with broadband frequency content. As a result, nonlinear piezoelectric harvesters are developed to harvest energy across a wide frequency band. For example, bistable piezoelectric material-based vibration energy harvesters are nonlinear devices with two equilibria, capable of producing large-amplitude motion between the two equilibria where mechanical energy that can be converted to electrical power. An inverted beam with a tip mass can be designed to be bistable and harvest vibrational energy at low frequencies. The tip mass can be selected to place the inverted beam near buckling to cause large geometrically nonlinear deformations at low excitation frequencies. The mathematical modeling dynamical behavior of an inverted beam with a tip mass has been previously investigated. This paper explores the effects of piezoelectric material nonlinearity and hysteresis on the harvested power of an inverted beam vibration energy harvester. This paper utilizes the Bouc-Wen model to describe the nonlinearity and hysteretic behavior of the piezoelectric material. The governing electromechanical equation of motion for an inverted beam energy harvester is derived which includes piezoelectric hysteresis effect as a function of strain. Numerical simulations are presented to show how the piezoelectric material hysteresis changes the harvested electrical power for different excitation amplitudes and frequencies. This paper improves existing nonlinear electromechanical models to produce more accurate results by modeling piezoelectric material hysteresis.