宽带随机激励下单自由度双边非对称碰撞振动系统的稳态响应  

STATIONARY RESPONSES OF A SINGLE-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM WITH TWO-SIDED ASYMMETRIC BARRIER IN THE PRESENCE OF WIDE-BAND NOISE

作　　者：王剑龙 冷小磊[1] 刘先斌[1] Wang Jianlong;Leng Xiaolei;Liu XianBin(Nanjing University of Aeronautics and Astronautics,State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing 210016,China)

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016

出　　处：《动力学与控制学报》2018年第4期338-343,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金(11172127)资助项目~~

摘　　要：本文以一类单自由度双边非对称碰撞振动系统为研究对象,采用广义Hertz接触模型表示碰撞过程,考察系统在宽带随机激励下的稳态响应.应用基于广义谐和函数的随机平均法推导出系统在宽带随机外激励下的伊藤随机微分方程,通过求解相应的稳态FPK方程,得到系统关于幅值、能量和位移的稳态概率密度以及位移与速度的联合稳态概率密度.另外,将系统的随机响应近似为马尔可夫过程,利用广义胞映射法得到系统的近似稳态响应.最后通过与蒙特卡罗模拟结果的对比,验证了随机平均法和广义胞映射法的有效性.In this paper,the stationary responses of a single-degree-of-freedom inelastic vibro-impact system with twosided asymmetric barrier in the presence of wide-band noise are studied. The generalized Hertz contact model is applied to simplify the impact restoring force of the vibro-impact system. The averaged Ito stochastic differential equation of the system under wide-band random excitation was obtained through the stochastic averaging method,based on the generalized harmonic functions. After solving the stationary FPK equation corresponding to the stochastic differential equation,the stationary probability densities of amplitude,total energy,displacement and the joint probability density of velocity,and displacement of the system are gained immediately. In addition,the stochastic responses of the system are approximated as Markov processes,and the generalized cell mapping method is applied to derive the approximate stationary responses. It demonstrates that the results obtained by the stochastic averaging method and the generalized cell mapping method are in a great agreement with those from Monte Carlo simulation.

关 键 词：碰撞振动系统 广义Hertz接触模型 随机平均法 稳态概率密度 广义胞映射 

分 类 号：TH113.1[机械工程—机械设计及理论]