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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。
Decomposition of Stochastic Structural Expansion System Dynamic Equations has always been a stochastic problem in structural response. With the help of Gegenbauer polynomial approximation method, the problem of calculating the dynamic response of the system with random parameters is transformed into the equivalent calculation of the response of the extended system. Using fine integral to K_L decomposition of non-stationary random excitation filtering white noise, using K_L vector energy concentration characteristics, using a small amount of K_L vector to participate in the response of the extended system to obtain more accurate response, significantly improve the calculation s efficiency. The correctness of the method is verified by simulation, and the influence of the difference of probability density function of random parameters on the mean square of the response is studied. Some conclusions about the engineering reference value are obtained.