Numerical Analysis of Nonlinearities Due to Rigid End-stops in Energy Harvesters

This paper gives a numerical analysis of nonlinearities due to rigid, elastic mechanical end-stops in a vibrating energy harvester. Both an eigenvalue problem approach and time domain simulations are used. We consider two rigid end-stops limiting the motion of a proof mass. The dynamics are linear between the impacts which cause strong nonlinear behavior. Even though the output power varies little with change in acceleration amplitude, we find that there can be drastic changes in the proof mass motion with change of amplitude. In a wide range of acceleration amplitudes the phase space trajectories are very complicated and have periods much longer than the period of the vibration, some appearing chaotic. Only in a small range of amplitudes do we find simple periodic motion.