Affiliation:
1. Department of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, P. R. China
2. State Key Lab for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, P. R. China
Abstract
Vibration impact is often used in the piezoelectric energy harvesting (PEH) system to increase the effective bandwidth of the harvester. Viscoelastic materials have been used successfully to mitigate vibration problems in various types of mechanical systems such as buildings, cars, aircraft and industrial equipment. However, less research has been done on the energy harvesting system with impact and viscoelastic force driven by random excitation. Stochastic response of an impact PEH system with viscoelastic force under Gaussian white noise excitation is investigated in this paper. Firstly, by transforming the variables, viscoelastic force can be substituted with the stiffness and damping terms to get an approximately equivalent system without viscoelastic term. Secondly, the approximate analytical solutions are acquired by the stochastic averaging method and nonsmooth coordinate transformation. The validity of this theoretical approach is confirmed by comparing the analytical solutions with the numerical solutions derived from the Monte Carlo method. Then, the effect of noise intensity and nonlinear damping coefficient on the stochastic response of the system is discussed. It is concluded that the restitution coefficient, viscoelastic component, relaxation time and linear damping coefficient can induce the occurrence of stochastic P-bifurcation. Finally, the roles of system parameters on the mean square voltage and average output power of the energy harvester are investigated respectively.
Funder
National Natural Science Foundation of China
Project of Science and Technology of Guangzhou
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)