随机结构在随机激励作用下的结构响应具有随机不确定性,响应的分布函数(CDF)能够充分地体现响应量分布变化规律,只要掌握了响应的CDF,就可以进一步掌握响应的统计信息。基于响应的CDF,对基本变量的分布参数进行灵敏度分析,可以表明基本变量的随机不确定性对输出响应的随机不确定性的影响程度,从而清楚地表明重要随机变量和非重要随机变量,为降低变量维数和优化设计提供依据。针对承受阵风激励的典型喷气运输机(BAH)的机翼,采用近似解析法、Monte Carlo模拟(MCS)法以及本文所建立的分层线抽样(SLS)方法对机翼的翼根弯矩(RBM)进行CDF求解,并进行CDF的灵敏度分析,通过分析得到第二阶和第五阶模态的质量和频率对阵风响应的CDF影响较大的结论。
Uncertainty of structural parameters will lead to the uncertainty of responses of stochastic structures with stochastic excitation. The cumulative distribution function (CDF) of the response can adequately reflect the response quantity distribution. Once the CDF of the response is mastered, its statistical information may be further grasped. A sensitivity analysis of the distributed parameters of the basic variable based on the CDF of response may indicate its influence on the stochastic uncertainty of the output response, This approach shows clearly the important random variables and non-important random variables, thereby reducing the variable dimension and providing basis for design optimization. This paper employs the approximate analytical method, Monte Carlo simulation (MCS) method and a novel stratified line sampling (SLS) method to solve the CDF of the root bending moment (RBM) of a typical random BAH jet transport aircraft wing with gust excitation and the corresponding sensitivity. It is found that the masses and frequencies of the second and fifth order modals have comparatively larger influence on the CDF of gust response.
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