【摘要】 对于受演变随机白噪声或有色噪声激励的结构，对其方差矩阵推导了相应的微分Ｌｙａｐｕｎｏｖ方程，并用精细积分方法建立了倍步长与等步长积分格式，使一大类以往难于得到精确解的问题，能迅速地在计算机上得到具有很高精度的解答。并用其它文献上的例题验证了本文给出方法的精确性及极高的计算效率。更多还原

【Abstract】 For most engineering structures subjected to stationary/nonstationary random excitations, the computations of their response variances are usually very difficult and time consuming. The PEM(pseudo excitation methods)have partly solved this problem by means of accurate and very efficient computations of various response power spectral densities which are used in the integration of the corresponding variances. This article shows that for some kinds of evolutionary white or colored random excitations, the Lyapunov equation of any arbitrary response variance matrix can be quickly and accurately computed in terms of the “precise integration scheme”, and thus further remarkably accelerates such computations. The corresponding stationary response variances can be conveniently obtained by using the double step formulas.更多还原