## 留言板

 引用本文: 马国亮, 徐明龙, 陈立群, 丁虎. 末端质量作用下变长度轴向运动梁的振动特性[J]. 应用数学和力学, 2015, 36(9): 897-904.
MA Guo-liang, XU Ming-long, CHEN Li-qun, DING Hu. Vibration Characteristics of an Axially Moving Variable Length Beam With a Tip Mass[J]. Applied Mathematics and Mechanics, 2015, 36(9): 897-904. doi: 10.3879/j.issn.1000-0887.2015.09.001
 Citation: MA Guo-liang, XU Ming-long, CHEN Li-qun, DING Hu. Vibration Characteristics of an Axially Moving Variable Length Beam With a Tip Mass[J]. Applied Mathematics and Mechanics, 2015, 36(9): 897-904.

• 中图分类号: O32

## Vibration Characteristics of an Axially Moving Variable Length Beam With a Tip Mass

Funds: The National Natural Science Foundation of China(11172229)
• 摘要: 对带集中质量，变长度(或速度)轴向运动梁的振动特性采用两种精确方法求解.首先，对变长度轴向运动Euler(欧拉)梁横向自由振动方程进行化简，通过复模态分析得到本征方程，并在有集中质量的边界条件下得到频率方程，用数值方法求解固有频率和模态函数.然后，采用有限元方法建立运动梁自由振动的方程，求解矩阵方程得到复特征值和复特征向量，结合形函数得到复模态位移.最后，将两种方法的计算结果进行了分析和对比.数值算例的结果表明：不同的轴向运动速度和集中质量对变长度轴向运动梁的振动特性有显著影响，两种计算方法的结果接近且均有效.
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##### 出版历程
• 收稿日期:  2015-04-24
• 修回日期:  2015-06-15
• 刊出日期:  2015-09-15

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