精细积分时域平均法和随机扩阶系统法

讨论含随机参数结构的动力响应的计算问题，发展了精细积分时域平均法（ＴＡＰＩＭ），它可以用来计算确定性系统受到随机激励时的动力响应；结合随机扩阶系统方法与随机有限元法，将ＴＡＰＩＭ方法应用于计算随机参数结构的动力响应，取得了较好的结果。结出了数值算例，结果表明随机扩阶系统法，随机有限元法与精细积分时域平均法的结合是计算 随机参数结构动力响应的有效方法。

TIME-DOMAIN AVERAGING OF PRECISE INTEGRATION AND STOCHASTIC SYSTEMORDER-EXPANSION METHOD

The direct integration methods in time domain for dynamic response computation of stochastic parameter structures subjected to random excitation were investigated in this paper. At first, based on High Precise Integration (HPI) method, which was developed originally for linear and deterministic system, a Time-domain Averaging Scheme of HPI (TAPIM) was developed to calculate the dynamic response of deterministic structure subjected to random excitation. In the second part of the paper, by using of Stochastic Finite Element Method (SFEM) combined with System Order-expanded Method (SOM), the system dynamic equation were obtained for an uncertain system with stochastic structural parameters, then the TAPIM was used to obtain the stochastic response of the system. Some numerical examples were given, including a two-degree of freedom linear system and a cantilever beam with stochastic structural parameters. Furthermore, a non-linear system of TDOF was computed combined with the statistical linearization method. The results showed that the integrated method of TAPIM, SFEM, and SOM can be used to compute the stochastic dynamic response of uncertain structure, the accuracy and efficiency of computation are much better than other traditional numerical integration methods.