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The Analysis of Dynamic Response Bounds of an Elastic Beam Subjected to an Uncertain Moving Load and Its Applications

DOI：

 作者 单位 E-mail 段民封 湖南大学 minfeng_duan@hnu.edu.cn 姜潮 湖南大学 jiangc@hnu.edu.cn 李金武 湖南大学 倪冰雨 湖南大学

不确定性移动载荷激励下的弹性梁振动是土木、机械和航空航天等工程领域普遍存在的一类重要问题。考虑到在许多实际工程中，不确定移动载荷的样本测试数据有限或测试成本较高，本文引入作者近期提出的区间过程模型对此类动态不确定性参数进行描述，提出了一种求解不确定移动载荷激励下弹性梁振动响应边界的非随机振动分析方法。首先，介绍了确定性移动载荷激励下弹性梁的振动微分方程及其解析求解方法；其次，引入区间过程模型，以上下边界函数的形式对不确定性移动载荷进行度量，进而基于模态叠加法发展出弹性梁振动响应边界求解的非随机振动分析方法；最后，将上述非随机振动分析方法应用于车桥耦合振动问题，分析和讨论了各参数对桥梁动态响应边界的影响。

The vibration of elastic beam under uncertain moving load is one of the most important problems in engineering such as civil, mechanical and aerospace. Given that the samples and uncertainty information of the moving load are inadequate in a lot of practical engineering problems, this paper quantifies the uncertain moving load by interval process model which has been proposed by the authors recent years, and then a non-random vibration analysis method for an elastic beam excited by an uncertain moving load is developed. This paper firstly introduces the vibration differential equation of an elastic beam subjected to a deterministic moving load and its deterministic response of the beam in the form of analytic expression. Secondly, the interval model is applied to measure the uncertainty of the moving load, and then the analytic expression of the dynamic response boundaries of the elastic beam system is derived based on modal superposition method. Subsequently, the interval of the dynamic uncertain response is obtained. Finally, a typical engineering problem, the uncertain vibration of the bridge due to the interaction of vehicle-bridge system is researched in detail. The impact of speed, correlation and system damping on the dynamic response of the bridge is investigated systematically.
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