Response Analysis of the Tristable Energy Harvester with an Uncertain Parameter

Abstract

In the stage of modelling, measuring, mechanical processing and manufacturing of the nonlinear energy harvesting system, deviations and errors of system parameters are inevitable. Even slight variation of key parameters may have a significant influence on the output voltages, especially for the multi-stable nonlinear case. Therefore, the investigation of dynamic behaviors for the tristable energy harvesting system with uncertain parameters is of important value both for research and application. In this paper, the uncertainty of a tristable piezoelectric vibration energy harvester with a random coefficient ahead of the nonlinear term is studied. By using the Chebyshev polynomial approximation, this tristable energy harvesting system is first reduced into an equivalent deterministic form, the ensemble mean responses of which are derived to exhibit the stochastic behaviors. The periodic and chaotic motions, bifurcations and crises under different conditions are analyzed. The results show that the output voltage is sensitive to the uncertainty of the nonlinear coefficient, which leads to unstable behavior around the bifurcation and crisis points particularly. Exploring the influence pattern of uncertain parameters on the output voltage and avoiding the unstable parameter intervals are essential for optimizing the structure. It can further improve the efficiency of the nonlinear energy harvesting system.