东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2017, Vol. 38 ›› Issue (1): 86-90.DOI: 10.12068/j.issn.1005-3026.2017.01.018

• 机械工程 • 上一篇    下一篇

一种复杂机械结构的频率可靠性及灵敏度分析方法

马天政， 吕昊， 张义民   

  1. (东北大学 机械工程与自动化学院， 辽宁 沈阳110819)
  • 收稿日期:2015-08-05 修回日期:2015-08-05 出版日期:2017-01-15 发布日期:2017-01-13
  • 通讯作者: 马天政
  • 作者简介:马天政(1987-)，男，辽宁鞍山人，东北大学博士研究生; 张义民(1958-)，男，吉林长春人，东北大学教授，博士生导师，教育部"长江学者"奖励计划特聘教授.
  • 基金资助:
    国家自然科学基金资助项目(U1234208)； 中央高校基本科研业务费专项资金资助项目(N02090022115014)； 国家重点基础研究发展计划项目(2014CB046303)； 国家自然科学基金重点资助项目(51135003)； “高档数控机床与基础制造装备”科技重大专项( 2013ZX04011011).

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

MA Tian-zheng， LYU Hao， ZHANG Yi-min   

  1. School of Mechanical Engineering & Automation， Northeastern University， Shenyang 110819， China.
  • Received:2015-08-05 Revised:2015-08-05 Online:2017-01-15 Published:2017-01-13
  • Contact: ZHANG Yi-min
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摘要： 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.

关键词: 频率可靠性, 可靠性灵敏度, 随机响应面, 降维积分, 模型降阶

Abstract: 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.

Key words: frequency reliability, reliability sensitivity, stochastic response surface, dimension reduction integral, model order reduction

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