能量包线随机平均法在汽车非线性系统中的应用

Application of Stochastic Averaging Method of Energy Envelope in Nonlinear Vehicle System

研究了能量包线随机平均法在汽车单自由度悬架迟滞非线性系统的应用。首先,建立了悬架单自由度迟滞非线性系统的动力学方程;其次,利用能量包线随机平均法得到关于哈密顿函数的平均伊藤随机微分方程,并得到与之相对应的稳态FPK方程,解得平稳位移和速度的联合概率密度,及平稳位移和速度的概率密度。发现在汽车迟滞非线性系统的随机响应中,能量包线随机平均法是一种有效的分析方法。

The method of stochastic averaging of energy envelope in the hysteretic vehicle suspension system with singledegree-of-freedom is studied.Firstly,the kinetic equation of the hysteretic suspension system with single-degree-of-freedom was established.Secondly,the method of stochastic averaging of energy envelope was used to obtain averaged Ito stochastic differential equations about Hamiltonian,and the corresponding steady FPK(Fokker-Planck-Kолмогоров)equation was got,the joint probability density of stable displacement and velocity were solved,as well as steady probability density of displacement and velocity.It is found that the method of stochastic averaging of energy envelope is an effective method to the random response of hysteretic vehicle system.