Parametric optimization of a frequency-up-conversion piezoelectric harvester via discontinuous analysis

Abstract

In this study, the dynamical and electrical behaviors of an impact-based frequency-up-conversion energy harvester were studied based on discontinuous dynamics theory. This analytical study enables us to better understand the response of an impact-based frequency-up-conversion energy harvester as system parameters change, hence, guiding us to design a high-efficiency energy harvester via optimizing the values of the critical parameters of the system. For a given base excitation, the optimum gap to maximize the output power was obtained. The energy harvester consists of a sinusoidal vibrating piezoelectric bimorph and a stopper. The equations of the piezoelectric bimorph, which was modeled as an Euler–Bernoulli beam, were obtained based on the linear piezoelectric constitutive law. The generated voltage and power of the energy harvester were obtained via discontinuous dynamics analysis. Furthermore, the bifurcation diagrams of period-1 and period-2 motions were presented as the excitation frequency varying. To better understand the effect of different parameters on the performance of our system, the bifurcation trees of the period-1 motion versus varying excitation frequency were analytically obtained for different initial gap distances between the piezoelectric beam and the stopper. In addition, the bifurcation diagram of period solutions with a constant excitation frequency and varying gap distance was also attained.