Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise

Because of the increasing demand for electrical energy, vibration energy harvesters (VEHs) that convert vibratory energy into electrical energy are a promising technology. In order to improve the efficiency of harvesting energy from environmental vibration, here we investigate a hybrid VEH. Unlike previous studies, this article analyzes the stochastic responses of the hybrid piezoelectric and electromagnetic energy harvesting system with viscoelastic material under narrow-band (colored) noise. Firstly, a mass-spring-damping system model coupled with piezoelectric and electromagnetic circuits under fundamental acceleration excitation is established, and analytical solutions to the dimensionless equations are derived. Then, the formula of the amplitude-frequency responses in the deterministic case and the first-order and second-order steady-state moments of the amplitude in the stochastic case are obtained by using the multi-scales method. The amplitude-frequency analytical solutions are in good agreement with the numerical solutions obtained by the Monte Carlo method. Furthermore, the stochastic bifurcation diagram is plotted for the first-order steady-state moment of the amplitude with respect to the detuning frequency and viscoelastic parameter. Eventually, the influence of system parameters on mean-square electric voltage, mean-square electric current and mean output power is discussed. Results show that the electromechanical coupling coefficients, random excitation and viscoelastic parameter have a positive effect on the output power of the system.