Response Analysis Of Asymmetric Piezoelectric Energy Harvesting Systems Under Stochastic Excitation

Random vibration phenomenon exists widely in all kinds of systems in nature.Understanding its dynamic response is critial for better understanding the natural world,which promotes the development and application of numerous research methods.Nowadays,most of the studies are for ideal cases where the system has a symmetric potential function.However,the error of measurement and fabrication process can lead to the asymmetric phenomenon of system potential energy function.Therefore,the analysis method for random response of asymmetric system has drawn the attention of many scholars.In this paper,the quasi-conservative stochastic averaging method based on coordinate transformation is developed to study the random response of cubic asymmetric monostable system under Gaussian white noise and Gaussian colored noise with correlation time,respectively.Firstly,the motion model of cubic asymmetric monostable piezoelectric vibration energy harvesting system is established according to the parameter relationship of potential energy functions.Subsequently,using a coordinate transformation,the asymmetric monostable system is decoupled into a single degree of freedom asymmetric system.Then,the Fokker-Plank-Kolmogorov(FPK)equation of the total energy is obtained under Markov approximation,and the expressions of the steady-state probability density function,mean square voltage and average output power are obtained by solving the FPK equation.Finally,the stochastic response of asymmetric systems under different excitations are further analyzed,and the effectiveness of the proposed method is verified by Monte Carlo numerical simulation method.The results show that under Gaussian white noise,the increase of excitation intensity,system asymmetry and coupling coefficient can enhance the output power of the system,while the increase of cubic nonlinear coefficient and damping coefficient can reduce the output power of the system.Under Gaussian colored noise,the correlation time of noise and the asymmetry of the system play positive roles in promoting the output of mean square voltage,but the increase of cubic nonlinear coefficient can inhibit the output of mean square voltage.These results provide theoretical support for the wide application of piezoelectric vibration energy harvesting system.