中文摘要：

由于设计、建造以及测量等诸多不确定因素的影响，通常的有限元力学分析模型只是原型结构的一种均值近似。采用随机结构模型是更为合理的。本文应用随机矩阵模拟不确定线性动力系统有限元模型中质量阵、阻尼阵和剐度阵的随机不确定性，并进一步建立此类非参数概率系统在平稳随机外载作用下动力响应的虚拟激励高效求解算法。数值结果表明。均值有限元模型和随机矩阵模型的动力响应具有很大的差异。对于精细制造，模型的随机性是不能忽略的，本文提出的算法为此类问题求解提供了一条有效途径。

英文摘要：

Due to the uncertainties taking place in designs, constructions and measures, general finite el ement models are no more than approximations to original structures, and the random structural models are more reasonable. In this paper, the random uncertainties of the mass, damping and stiffness matri ces in the finite element model are modeled by random matrices, and a high efficiency pseudo excitation method for the dynamic responses analysis of the nonparametric probability system subjected to stationary random load is developed. A numerical example shows that the dynamic responses of the conventional （mean） finite element model are quite different from those based on the random matrix model. For precise manufacture, the uncertainties of models can not be ignored and the proposed method is quite useful in the analysis of such problems.