Stochastic Response and Bifurcation of a Two-Degree-of-Freedom Energy Harvesting System with Stoppers

It was shown previously that the synergy of the multi-degree-of-freedom (multi-DOF) and the mechanical stopper techniques is an effective way to further broaden the operation bandwidth of vibration energy harvesters. Considering the stochastic factor at the same time, this paper is devoted to developing a theoretical method for analyzing the dynamical characteristics of an impact-engaged 2DOF energy harvesting system under stochastic excitation, in which the impact is modeled as a nonlinear piecewise function. The existence of the impact and multi-DOF brings complexity in analyses, and the main theoretical method utilized in this paper is the stochastic averaging method which is suitable for multi-DOF quasi-nonintegrable systems. After that, the joint and marginal probability density functions of the system are derived, and numerical examples are shown to verify the effectiveness of the theoretical method. It is noteworthy that the theoretical method has the potential to be extended to more complex multi-DOF systems with stoppers. Subsequently, the stochastic response, bifurcations in the stochastic and corresponding deterministic systems, and the relationship between the D-bifurcation and the mean square voltage are discussed. Effects of crucial system coefficients, the impact stiffness and distance on the system are investigated as well.