The Study of Nonlinear Vibration of the Cantilever Beam Structure in Piezoelectric Energy Harvesters

Abstract

Piezoelectric vibration energy harvesters is have been frequently investigated in the past five years, cantilever beams with two piezoceramics layers are the most commonly used type. In this paper, the clamped-free beam is attached to a vibrating host structure and therefore it is subjected to a base excitation, while a proof mass is fixed at the free end. The excitation of the harvester is assumed to be due to its base motion in the form of translation in the transverse direction, for the sake of simplicity, it is restricted to be harmonic in time. Based on the Von Karman theory and Reddy higher order shear deformation theory, a cantilever piezoelectric beam dynamics equation derived from Hamilton principle. Using the method of Galerkin to discrete partial differential equations, single degrees of freedom nonlinear controlling equation is obtained, then, the method of asymptotic perturbation is used to determine to the averaged equation. Finally, a nonlinear analysis of the resonance response of the Cantilever beam is presented.