复合随机振动系统的动态可靠性分析  

Dynamic Reliability Analysis of Double Random Vibration System

作　　者：王倩倩[1] 张义民[1] 王一冰[1] 吕昊[1] 

机构地区：[1]东北大学机械工程与自动化学院,沈阳110819

出　　处：《振动．测试与诊断》2013年第4期670-675,727-728,共6页Journal of Vibration,Measurement & Diagnosis

基　　金：长江学者和创新团队发展计划资助项目(IRT0816);"高档数控机床与基础制造装备"科技重大专项课题资助项目(2010ZX04014-014);国家自然科学基金资助项目(50875039);中央高校基本科研业务费资助项目(N110603001)

摘　　要：针对随机结构在随机过程激励下的动态响应问题,利用Karhunen-Loève分解方法将随机激励过程分解为以Gauss-Legendre积分节点为时间点的一系列时域确定性函数与独立随机变量相组合的形式,同时结合基于Gauss-Legendre积分公式的精细时程积分方法,求得各时域确定性函数下的时域响应。运用点估计法,计算随机结构系统在确定性时域激励下响应的统计矩。考虑随机过程的随机性与结构随机性相互独立的特性,得到随机结构参数和随机激励复合随机作用下响应的统计矩,并利用可靠性分析的四阶矩方法计算了随机结构在随机激励下的动态瞬时可靠度。与Monte Carlo模拟方法的对比可以验证所提出方法的精确性。对动态瞬时可靠度的分析可以获得振动系统在瞬态受载过程中的薄弱时刻,通过改进结构设计能够避免系统在薄弱时刻的失效,为振动系统的瞬态可靠性评估提供了理论基础。The solution of the dynamic responses issue of systems with random structure parameters subjected to stochastic excitation is proposed.The stochastic process Karhunen-Loève decomposition method is used to express the excitation process into the form of a series of deterministic functions of time multiplied by independent zero mean standard random quantities,and the discrete points are made to be the same as Legendre quadrature points.Then the precise quadrature with Gauss-Legendre integration is used to solve the oscillation differential functions.Considering the independent relationship of the structural random parameters and the parameters of random process,the time-varying moments of the response are evaluated by the point estimating method.Combined with the forth moment method theory of reliability analysis,the dynamic reliability response can be evaluated.The result obtained by the proposed method is accuracy enough compared with the Monte Carlo simulation method.The dynamic reliability curve is useful for getting the weakness time so as to avoid broken at the weakness time.The method here provides a theoretical basis for the vibration system transient reliability assessment and improvement.

关 键 词：Karhunen-Loève分解 Gauss-Legendre积分 精细积分 点估计 可靠性 

分 类 号：TB114.3[理学—概率论与数理统计]