结构随机动力稳定性的定量分析方法

发布时间：2018-02-20 02:42

本文关键词： 随机动力稳定定量方法概率耗散系统概率密度演化方程　出处：《力学学报》2016年03期 　论文类型：期刊论文

【摘要】：提出了结构随机动力稳定性的定量分析方法,讨论了经典的随机动力稳定性概念,指出结构动力稳定性不仅与结构参数有关,也与作用在结构上的外部载荷密切相关,据此引入了一种判定结构动力稳定性的新准则,明确了结构随机动力稳定性的基本涵义.在概率守恒原理基础上,推导了概率耗散系统的广义概率密度演化方程.引入结构动力失稳的物理机制作为引起概率耗散的驱动力,利用概率耗散系统概率密度演化方程、可以方便获得结构响应的概率密度演化过程,从而定量求解结构的动力稳定概率.据此,可以定量评价结构系统依概率为1或依给定概率意义上的结构随机动力稳定性.采用本文所建议方法对典型结构动力系统进行了随机动力稳定性分析,并与蒙特卡洛方法计算结果进行对比.数值结果表明了所建议方法的有效性.
[Abstract]:A quantitative analysis method of stochastic dynamic stability of structures is presented. The classical concept of stochastic dynamic stability is discussed. It is pointed out that the dynamic stability of structures is not only related to structural parameters, but also closely related to the external loads acting on the structures. Based on this, a new criterion for determining the dynamic stability of structures is introduced, and the basic meaning of stochastic dynamic stability of structures is defined. The generalized probabilistic density evolution equation of probabilistic dissipative system is derived. The physical mechanism of structural dynamic instability is introduced as the driving force to cause probabilistic dissipation, and the probabilistic density evolution equation of probabilistic dissipative system is used. The probability density evolution process of the structural response can be obtained conveniently, and the dynamic stability probability of the structure can be calculated quantitatively. The stochastic dynamic stability of a structural system with a probability of 1 or a given probability can be quantitatively evaluated. The stochastic dynamic stability of a typical structural dynamic system is analyzed by using the method suggested in this paper. The numerical results show the effectiveness of the proposed method.
【作者单位】：同济大学土木工程学院;土木工程防灾国家重点实验室;
【基金】：国家自然科学基金资助项目(51261120374,91315301)
【分类号】：O316

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