Abstract
Parametric excitation is introduced to amplify the external harmonic excitation and extend the capabilities of a nonlinear piezoelectric energy harvester device. To investigate the efficiency of the parametrically amplified energy harvester, the time responses of the voltage and power are computed using the state space formulation. It is assumed that the proposed nonlinear model consists of cubic and quadratic nonlinearities, where parametric amplification appears in the form of a trigonometric function. The frequency is tuned as the one-to-one ratio between the external and parametric excitations. An optimal configuration of the nonlinear system is illustrated to achieve the maximum possible harvested energy. Next, the effect of parametric amplification on the harvested power is investigated considering system uncertainties. The complex nonlinear relationship is mapped with the help of a machine learning technique, namely a Gaussian process. Once these techniques are trained using a small number of samples, they emulate the stochastic nonlinear dynamical system without having to solve the actual governing equations. The results obtained by the proposed methodology are verified with results from direct numerical integration combined with Monte Carlo simulation.