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。

Abstract: An extended precise integration method for computing the non-stationary response of linear MDOF structure subjected to evolutionary random excitation is proposed. Random loads are first transformed into deterministic loads using Pseudo-excitation algorithm before precise and efficient recursive relations with unified form are constructed by using the precise computing method of Duhamel integration. The avoidance of inverse matrix computing makes the presented method independent to the nature of system matrix or its dynamic matrices, enhancing the numerical stability and expanding its applied scopes. The presented method enjoys the same high numerical precision as HPD-M and a higher efficiency than the expanding precise integration method. Examples are given to show advantages of this method.