Study On The Steady-state Probability Response Of Typical Asymmetric Stochastic System

Nonlinear structures and random forces exist widely in our life and engineering prac-tice,so nonlinear random dynamics model can reflect the real world natural system more perfectly and truly;In the actual system,its restoring force usually presents asymmetric physical characteristics,it is of scientific value and practical significance to study the effect of asymmetry on the dynamic behavior of system.In this paper,based on the Fourier series expansion of Jacobi elliptic function,a new stochastic averaging method is proposed to study the steady-state probability density of the response of asymmetric stochastic system under random excitation.Based on the Jacobi elliptic function,the average Ito stochastic differential equation of the system amplitude is obtained,and the corresponding Fokker-Planck-Kolmogorov(FPK)equation is established.Finally,the analytical expression of the steady-state probability density function is obtained.In Chapter 3,the typical examples under linear and nonlinear damping are taken as the re-search object,the steady-state probability density function of the system response excited by Gaussian white noise and Gaussian color noise is considered respectively,and the effec-tiveness of the method is verified by Monte Carlo numerical simulation.At the same time,the influence of the system parameter change on the steady-state response of the system is discussed in detail.The results show that among the many factors that affect the response of stochastic system,the intrinsic parameters of the system are not negligible.In particular,the probability response of asymmetric systems under different noise excitations is affected by the system parameters.The increase of noise intensity and stiffness coefficient under Gaussian white noise excitations may promote the steady-state response of the system;the increase of noise intensity under Gaussian colored noise excitations also enhances the steady-state behavior,while the correlation time and stiffness coefficient increase,the steady-state of the system is weakened.