受演变随机激励结构响应的扩展精细积分方法

摘要：对于受演变随机激励的线性多自由度体系，给出了计算其非平稳响应的扩展精细积分方法。首先采用虚拟激励法，将随机荷载转化成确定性荷载，然后采用Duhamel积分的精细计算方法，构造出统一形式的精确、高效递推格式。本文方法避免了矩阵的求逆运算，不依赖于系统矩阵或其动力矩阵的性态，提高了数值稳定性和应用范围。本文方法具有与混合型时程精细积分方法同样高的数值精度，而效率上要高于增维精细积分方法。算例验证了本文算法的优越性。

An extended precise integration method for response of a structure subjected to evolutionary random exciation

An extended precise integration method for computing the non-stationary response of a linear MDOF structure subjected to evolutionary random excitation was proposed. Random loads were firstly transformed into determinis- tic loads using a Pseudo-excitation algorithm before precise and efficient recursive relations with an unified form were con- structed using the precise computing method of Duhamel integration. The avoidance of inverse matrix computing made the presented method independent to the nature of the system matrix or its dynamic matrices, enhanced the numerical stability and expanded its applied scopes. The presented method had the same high numerical precision as HPD-M and a higher ef- ficiency than the dimension-expanded precise integration method. Examples were given to show advantages of this method.