Investigation of the exponentially tapering effect on the behavior of piezoelectric energy harvester including geometric, inertial, material and damping nonlinearities

In this paper, the nonlinear electromechanical formulations of a piezoelectric energy harvester are proposed to investigate the effect of exponential tapering on generating more power with less mass from energy harvester. For this purpose, geometric, inertial, material and damping nonlinearities are included. The governing equations are derived using the Euler-Bernoulli and linear variation of electric voltage along the thickness assumptions. The coupled nonlinear equations are discretized by the mass normalized mode shapes of an exponentially tapered piezoelectric beam with tip mass, and resulting differential equations are solved employing the method of multiple scales. An experiment is set up, and the damping coefficient of the beam is calculated from the tip acceleration to base acceleration frequency response function in the case of low exciting acceleration and short circuit. Material nonlinear coefficients are identified using the experiment, when the exciting acceleration of the shaker is increased, and the proposed solution accuracy is verified. The effect of tapering exponentially on the behavior of the piezoelectric energy harvester is investigated by studying length, tapering parameter and exciting acceleration amplitude in some examples.