An improved stochastic averaging process on a monostable piezoelectric vibrational energy harvester model excited by colored noise

A monostable piezoelectric vibration energy harvester (VEH) model subject to Gaussian colored noise is studied in this paper. With the help of energy balance method, a concise expression of the transient frequency which is determined by transient amplitude is used in the stochastic averaging process. Then an Itô stochastic differential equation is obtained. The new expression of frequency can lead to pretty good probability density function (PDF) of the displacement, PDF of output electric voltage of the VEH model, even if the nonlinear stiffness coefficient is very large. The influence of the nonlinear stiffness coefficient on the PDFs and on the output electric voltage is detailed and discussed. It is found that the larger nonlinear stiffness coefficient is, the smaller motion range and smaller mean square value of electric voltage it will result in. Furthermore, the larger time delay coefficient of the colored noise is, the larger mean square value of electric voltage it will lead to. Numerical simulations verified the accuracy of this method.