Nonlinear size dependent modeling and performance analysis of flexoelectric energy harvesters

Abstract

In this study, the effect of flexoelectricity on rectangular prismatic beams is analytically investigated when considering various boundary conditions including fixed–fixed, fixed–hinged, and hinged–hinged. The dynamical system undergoes harmonic loading and has the von Karman strain nonlinearity due to the mid-plane stretching. The beams are assumed to be long and slender, allowing for Euler–Bernoulli beam analysis to be conducted. To account for the size dependent effects of the material, Eringen’s nonlocal elasticity theory is employed. After determining the exact mode shapes, the Galerkin discretization is utilized to derive the nonlinear reduced-order model. The fixed–hinged model is the only model that can harvest power due to its lack of boundary condition symmetry and is the model that is heavily examined. The harvested power from the macro to the micro scales is small, as is expected; however, at the nanoscale the softening effect due to the nonlocality increases the nonlinear hardening behavior and decreases the system’s natural frequency. This allows for lower excitation frequencies to harvest energy, with a broader range of frequencies being able to harvest energy. Micro and macro scales do not exhibit any variation based on nonlocal effects, nor can they harvest significant amounts of power through flexoelectricity alone. These nano-devices can be developed and can produce significantly more energy than previously thought; but they require more advanced modeling techniques that necessitate a more thorough understanding of non-classical continuum mechanics and its coupling to nonlinear dynamics.