Hybrid electromagnetic and piezoelectric vibration energy harvester with Gaussian white noise excitation

In this work, we investigated the dynamical behavior of the hybrid energy harvester under Gaussian white noise using probabilistic approach. We find that under the influence of this kind of noise, the dynamics of the nonlinear electromechanical system exhibited the stochastic bifurcation which is characterized by a qualitative change of the stationary probability distribution. A stochastic averaging method is applied in this system in the aim to build the Itô Stochastic differential equations. From these equations, the Fokker-Planck Equations (FPE) of the electromechanical system is constructed whose the solution at the stationary state is a probability density. By combining the harmonic excitation to the random force, the harvested energy is improved. We also provided the optimization rate of the hybrid system with respect to the piezoelectric system. Besides, the comparison between the power obtained by the hybrid model, piezoelectric and electromagnetic energy harvester shows the interest to build the hybrid model. The analytical results agree very well with numerical simulation.