Nonlinear analysis of axially loaded piezoelectric energy harvesters with flexoelectricity

Abstract

In this work, nonlinear electromechanical models for energy harvesters based on axially preloaded piezoelectric beams incorporating flexoelectric effect are presented. Depending on the amplitude of the applied axial load, the proposed energy harvester could operate in either prebuckling or postbuckling configuration. According to the theory of flexoelectricity and the Hamilton's principle, the nonlinear electromechanical coupling equations of the proposed energy harvesters under base excitations are derived. For a simply-supported piezoelectric beam, the expression of the static buckling load is analytically determined. Then, for energy harvesters in the prebuckling and postbuckling configurations, we obtain the discrete nonlinear governing equations by employing the Galerkin's method. These coupling equations are solved numerically by the Runge–Kutta method. Case studies are provided to show the steady-state output voltage and power of the energy harvesters. Results indicate that the frequency response curves show a typical hardening nonlinear behavior in the prebuckling configuration and a softening nonlinear behavior in the postbuckling configuration. Such nonlinear behaviors of energy harvesters imply a wider frequency operation bandwidth of the proposed energy harvesters. We also find that the energy harvesters utilizing flexoelectricity have a better performance than those based on piezoelectricity in the prebuckling configuration. Moreover, we examine the influences of resistive load, mechanical damping coefficient and the amplitude of the base excitation on the performance of the energy harvesters as well as the size effect due to flexoelectricity. It is also interesting to observe that both intrawell and interwell oscillations of the energy harvesters could occur in the postbuckling configuration. This work provides an efficient route to design energy harvesting systems at micro- and nano-scales with enhanced performance.