一种复杂机械结构的频率可靠性及灵敏度分析方法

针对具有随机参数的复杂机械结构振动的固有频率响应问题,定义了频率可靠性,并在此基础上提出了一种快速有效的可靠性及可靠性灵敏度的计算方法.采用随机响应面模型来拟合结构输入参数和固有频率之间的函数关系,并使用降维积分技术计算随机响应面模型的展开系数,同时使用模型降阶方法来进行结构的重分析计算以节约计算时间.采用改进的一次二阶矩方法进行可靠性分析,可靠性灵敏度的计算采用蒙特卡洛模拟方法.数值算例表明所提方法具有很高的计算效率和合适的精度,适用于复杂结构的频率可靠性分析.

A Novel Approach to Compute the Frequency Reliability and Reliability Sensitivity for Complex Mechanical Structures

For the frequency response of complex mechanical structures with random parameters， the frequency reliability was defined and an efficient method to compute the frequency reliability and reliability sensitivity was proposed. The stochastic response surface was employed to approximate the relationship between input variables and natural frequency. Dimension reduction integral was utilized to compute the coefficients of the stochastic response surface expansion. In order to alleviate the computational burden of structural reanalysis， a kind of model order reduction technique was applied. The AFOSM (advanced first order second moment) method was utilized to evaluate the frequency reliability and the reliability sensitivity was obtained by the Monte Carlo simulation. The numerical examples demonstrate the efficiency and accuracy of the method for complex structures.