Modal reduction-based finite element method for nonlinear FG piezoelectric energy harvesters

Abstract

In this study, harvesting energy from a nonlinear functionally graded (FG) piezoelectric cantilever beam under harmonic excitation is investigated. The material properties of the piezoelectric are assumed to be a combination of piezo-ceramic and piezo-polymer materials for high performance and flexibility. The neutral axis is obtained in order to eliminate bending–stretching coupling. The geometrical nonlinearity and electromechanical coupling are incorporated in the coupled nonlinear equations that are derived using the generalized Hamilton’s principle and solved using the combination of modal reduction and finite element methods. The shooting method is employed to obtain steady-state periodic response of an FG nonlinear harvester with appropriate initial conditions. Also it is shown that at least two-mode approximation is required for accurate estimation of nonlinear response and harvested power. Using the method of nonlinear modal reduction, the unstable branches for frequency domain solution are estimated and the computational time is reduced considerably compared to full finite element method. A case study is also accomplished in detail to analyze the effects of base amplitude values and material distribution on harvested power and bandwidth.