给出不确定性激励下的动态响应边界--一种非随机振动分析方法

GIVING DYNAMIC RESPONSE BOUNDS UNDER UNCERTAIN EXCITATIONS——A NON-RANDOM VIBRATION ANALYSIS METHOD

提出了一种非随机振动分析方法,可给出系统在不确定性激励下的动态响应边界,从而为实验信息相对缺乏的不确定性振动分析及未来的可靠性设计提供一种新的计算工具.采用非概率凸模型过程而非传统的随机过程描述不确定性动态激励,仅需知道激励在任意时刻点的边界信息而非精确概率分布,从而有效降低对大样本量的依赖性.针对单自由度和多自由度系统,建立了相应的非随机振动分析算法,以求解系统在不确定性动态激励下的响应区间;另外,也给出了蒙特卡罗仿真方法,为非随机振动提供一种最为一般的分析工具.最后,通过3个数值算例验证了本文方法的有效性.非随机振动分析方法可以作为传统随机振动理论的补充,在工程不确定性结构动力学分析及结构可靠性设计领域发挥作用.

A non-random vibration analysis method is proposed in this paper, which calculates the dynamic response bounds of vibrational systems under time-variant uncertain excitations. It provides a prominsing alternative computational tool for uncertain vibration analysis in case of lack of experimental information and the corresponding reliability design in the future. The non-probabilistic convex model process, rather than traditional stochastic process, is used to describe uncertain dynamic excitations because the former needs only the bound information instead of precise probability distribution at any time point and therefore dependence on large sample size is weakened effectively. Based on the convex model process, non-random vibration analysis algorithms are formulated to obtain dynamic response bounds of SDOF system and MDOF system under time-variant uncertain excitations, respectively. Besides, corresponding Monte Carlo method is proposed to verify accuracy of the response bounds calculated and provide a general analytical tool for non-random vibration analysis. Finally, the feasibility of the non-random vibration analysis method is validated by several numerical examples. The proposed non-random vibration analysis method could provide a promising supplementfor random vibration theory, and thereby plays an important role in structural uncertain dynamic analysis and reliability design.for engineering problems.