Nonlinear Oscillations and Frequency Responses of Cantilevered Piezoelectric Vibration Energy Harvesters

In this paper, cantilevered beam with piezoelectric layers are considered as the mechanical model of vibration energy harvesters. This paper aims to investigate the complicated dynamics behavior of the nonlinear vibrations of the cantilevered piezoelectric beam. The base excitation on the harvester beam is assumed to be harmonic load. Based on the third-order shear deformation theory and the Hamilton’s principle, the nonlinear equations of motion for the cantilevered piezoelectric beam are derived. The Galerkin’s approach is employed to discretize the partial differential equations to the ordinary differential equations with one-degree-of-freedom. The method of multiple scales is used to obtain the averaged equations in the polar form. Based on the actual work situation of the cantilevered piezoelectric beam, it is known that the base excitation plays an important role in the nonlinear vibration of the cantilevered piezoelectric beam. From the averaged equations obtained, numerical simulations are presented to investigate the effects of parameters on the steady-state responses of the cantilevered piezoelectric beam. We analyze the influences of the excitation magnitude, the excitation frequency, the piezoelectric material parameter and the damping parameter on the steady-state responses of the cantilevered piezoelectric beam. In addition, it is observed that the base excitation has significant influence on the nonlinear dynamical behavior of the cantilevered piezoelectric beam.