Explorations of displacement and velocity nonlinearities and their effects to power of a magnetically-excited piezoelectric pendulum

This paper explores the relation of the nonlinearities of displacement and velocity dynamics with the power of a piezoelectric pendulum under a periodic magnetic excitation. Initially, the theoretical formulation including the mechanical, magnetic and electrical terms is realized. Then a simulation study has been done by using the theoretical formulation based on the experimental parameters. Then, a detailed experimental survey has been carried out for some representative system parameters. Results of simulation based on the proposed model are presented and compared with the experimental results. It is observed that the periodic magnetic flux can cause different responses from regular dynamics to chaotic one. Phase space constructions, Poincare sections and FFTs are determined on parameter sets including the excitation frequency f and amplitude U-c of electromagnet. It is proven that the periodic magnetic flux exerts high frequency velocity fluctuations nearby the minimal and maximal values. While the displacement of the tip exhibits a harmonic fluctuation, FFFs prove the high frequency responses in addition to the main frequency. When f differs from the natural frequency of the system f(0), the responses become chaotic. It is proven that lower and higher frequency fluctuations in displacement and velocity, which are different from f(0) decrease the electrical power harvested by the piezoelectric pendulum. However, in the case of rms values of displacement/velocity, the harvested power is perfectly proportional to the rms values. Therefore, useful relations between power and rms values of displacement/velocity have been determined for the estimation of power output in such systems for the first time. The piezoelectric pendulum harvests much energy when f is closed to f(0) and the distance to the magnetic device should be closer in order to decrease the nonlinearities in displacement and velocity. (C) 2015 Elsevier B.V. All rights reserved.