随机结构非平稳响应的正交解法

THE ORTHOGONAL METHOD FOR RANDOM STRUCTURAL NON-STATIONARY RESPONSE

解随机结构扩阶系统动力方程一直是随机结构响应求解中的难点。借助Gegenbauer多项式逼近法,将随机参数系统动力响应计算问题转化为与其等价的确定扩阶系统的响应计算问题。用精细积分对过滤白噪声的非平稳随机激励进行K_L分解,利用K_L向量的能量集中的特点,用少量的K_L向量参与扩阶系统的响应计算即可获得较精确的响应值,显著提高了计算的效率。仿真验证了方法的正确性,并对随机参数概率密度函数的差异对响应均方值的影响等进行了研究,获得了一些有工程参考价值的结论。

Solving an expanded order-system dynamic-equation is the difficulty to obtain the dynamic response of a random structure.By using Gegenbauer polynomial approximation,the calculation problem of dynamic responses of a random parameter system is transformed to system＇s response calculation of an equivalent order certainty expansion.The Precise Integration Method is used to obtain the K_L decomposition vectors of the non-stationary filtered white noise random excitation,with characteristics of energy concentration,a small amount of K_L vector used to compute response of the extended order system can obtain a very accurate result,and it significantly improves the calculation efficiency.Simulation verifies the correctness of the method,and the effects of the probability density function of random parameters to the response mean square value are studied,and some engineering valuable conclusions are obtained.