Coherence resonance of piezoelectric energy harvester with fractional damping

In this paper, we investigate the coherence resonance of a piezoelectric energy harvester of beam subjected to an axial force. The fractional damping is considered. First, a nonlinear model of the energy harvesting system with fractional damping and random excitation is set up. The coupling equations of dynamics and electrics are derived. Euler- Maruyama-Leipnik method is used to solve the fractional order differential equations. The signal-to-noise ratios, mean responses, and other statistical quantities under the damping forces with different orders are computed. The results obviously show the appearance of coherence resonance. It can be seen that the reduction of fractional order not only reduces the critical value of noise level, thus leading to coherence resonance, but also increases the amplitude on the occurrence of coherence resonance. So it is possible to maximize harvest power for a given density or variance of random excitation by varying system parameters.