## 留言板

 引用本文: 朱丹阳, 张亚辉. 基于有限元和Duhamel积分的移动力问题分析方法研究[J]. 应用数学和力学, 2014, 35(12): 1287-1298.
ZHU Dan-yang, ZHANG Ya-hui. A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1287-1298. doi: 10.3879/j.issn.1000-0887.2014.12.001
 Citation: ZHU Dan-yang, ZHANG Ya-hui. A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1287-1298.

• 中图分类号: O326

## A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads

Funds: The National Natural Science Foundation of China（11172056）;The National Basic Research Program of China (973 Program)（2014CB046803）
• 摘要: 针对桥梁在移动力作用下的动力响应问题，提出了一种基于有限元模型和Duhamel积分的半解析分析方法，以此为基础，推导了多个移动力作用下桥梁动力响应的共振和相消条件.该方法基于桥梁有限元模型的振型，通过单元形函数构造桥面分段连续振型，得到Duhamel积分在任意桥面单元内的解析表达，将时间变量从被积函数中分离出去并利用积分的可加性，使得前面时刻的积分不必重复计算，因此每一个计算时间节点仅需计算一次简单积分和一次求和，这样极大地减少了计算时间.该方法在计算中未引入任何近似，且其精度与时间积分步长无关，是有限元模型下的解析解答.在数值算例中，分别针对简支梁和三跨连续桥梁，通过与解析解和Newmark法的对比，验证了该方法的精确性；然后针对多个移动力问题，验证了桥梁动力响应的共振和相消条件，探讨了载荷间距对复杂结构动力响应共振和相消的影响.
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##### 出版历程
• 收稿日期:  2014-10-08
• 修回日期:  2014-10-21
• 刊出日期:  2014-12-15

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