摘要
用拟不可积哈密顿系统随机平均法研究了二自由度碰撞振动系统的随机响应。先将二自由度随机激励的碰撞振动系统表示成随机激励的耗散的哈密顿系统形式 ,然后用拟不可积哈密顿系统的随机平均法得到了以系统哈密顿函数为基本变量的一维 Ito随机微分方程 ,最后用数值方法求解与该方程相应的稳态 FPK方程 ,得到系统响应的平稳概率密度。
A stochastic response of two degree of freedom vibro impact system is studied by using the stochastic averaging method for quasi non integrable Hamiltonian systems. Firstly, a stochastically excited 2 DOF vibro impact system is formulated as a stochastically excited and dissipated Hamiltonian system. Secondly, the system is reduced to a averaged It stochastic differential equation for Hamiltonian using the stochastic averaging method for quasi non integrable Hamiltonian systems. Finally, the probability density of stationary response of the system is obtained for two special cases. Numerical results are compared with those from digital simulation to verify the applicability of the stochastic averaging method for the analysis of the stochastic response of 2 DOF vibro impact systems.
出处
《振动工程学报》
EI
CSCD
北大核心
2002年第3期257-261,共5页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目 (编号 :10 0 0 2 0 15 19972 0 5 96 0 0 340 10 )
关键词
自由度
碰撞激发
随机平均法
随机响应
碰撞振动
impact excitation
vibration effect
stochastic averaging method
stochastic response
