The stationary response of piezoelectric cantilever beam model excited by colored noise

This article provides a method to predict the steady-state response of a piezoelectric cantilever under the excitation of Gaussian colored noise which is a better approximation to the ambient random excitation than the white noise. In this paper, a cantilever energy harvester model, which is fully-paved with piezoelectric ceramic and excited by Gaussian colored noise, is built by the Lagrange’s equations and is nondimensionalized. Then the dynamic equation and piezoelectric equation are transformed into a pair of stochastic differential equations about transient equivalent amplitude and transient phase. After that, the stochastic averaging method is applied to simplify the stochastic differential equations into an Itô type equation about the equivalent amplitude, the drift coefficient and the diffusion coefficient are obtained. This method provides another approach which is different from the stochastic linearization method and moment method. On this basis, some crucial outputs such as the steady-state probability density function (PDF) of the equivalent amplitude, the beam’s displacement, the transient output voltage, the joint probability density function of displacement and velocity as well as the mean square value of output voltage are all obtained. With different noise intensity values and delay factors, the Monte Carlo numerical simulation has verified the correctness of the theoretical prediction.