## 留言板

 引用本文: 鲍四元, 邓子辰. 由纵向振动引起的质点与圆锥形杆碰撞问题的解析解[J]. 应用数学和力学, 2006, 27(7): 812-818.
BAO Si-yuan, DENG Zi-chen. Analytical Solutions for Response of Collision of Particle With Conical Rod Caused by Longitudinal Vibration[J]. Applied Mathematics and Mechanics, 2006, 27(7): 812-818.
 Citation: BAO Si-yuan, DENG Zi-chen. Analytical Solutions for Response of Collision of Particle With Conical Rod Caused by Longitudinal Vibration[J]. Applied Mathematics and Mechanics, 2006, 27(7): 812-818.

## 由纵向振动引起的质点与圆锥形杆碰撞问题的解析解

###### 作者简介:鲍四元(1980- ),博士(E-mail:bsiyuan@mail.nwpu.edu.cn);邓子辰(1964- ),教授,博士生导师(联系人.Tel:+86-29-88460403;E-mail:dweifan@nwpu.edu.cn).
• 中图分类号: V214.2

## Analytical Solutions for Response of Collision of Particle With Conical Rod Caused by Longitudinal Vibration

• 摘要: 给出细长圆锥形的截面杆受到质点纵向碰撞时的精确解析解．提出了一种新方法用于分析质点-圆锥形杆碰撞，使用了叠加法给出杆的响应．其结果可验证数值解和其他解析解．所提出方法的优点之一是响应解的解析形式简洁．结论是质量比和一些描述杆几何形状的变量，如倾斜度、杆长和半径在撞击分析中具有重要作用．
•  [1] Goldsmith W.Impact:the Theory and Physical Behaviour of Colliding Solids[M].London:Edward Arnold Ltd,1960. [2] Graff K F.Wave Motion in Elastical Solids[M].Oxford: Clarendon,1975. [3] HU B,Eberhard P,Schiehlen W.Symbolic impact analysis for a falling conical rod against the rigid ground[J].Journal of Sound and Vibration,2001,240(1):41—57. [4] HU Bin,Eberhard Peter.Symbolic computation of longitudinal impact wave[J].Comput Methods Appl Mech Engrg,2001,190(3):4805—4815. [5] Timoshenko S.Vibration Problems in Engineering[M].2nd ed.New York: Van Nostrand,1937. [6] Sankzn,Yuganva.Longitudinal vibrations of elastic rods of stepwise-variable cross-section colliding with a rigid obstacle[J].J Appl Maths Mechs,2001,65(3):427—433. [7] 诸德超，邢誉峰.点弹性碰撞问题之解析解[J].力学学报，1996,28(1):99—103. [8] ZHU De-chao，XING Yu-feng.Analytical solution of impact problems of rod structures with springs[J].Comput Methods Appl Mech Engrg,1998,160(2):315—323. [9] Abrate S.Vibration of non-uniform rods and beams[J].Journal of Sound and Vibration,1995,185(4):703—786. [10] Kumar B M,Sujith R.Exact solutions for the longitudinal vibration of non-uniform rods[J].Journal of Sound and Vibration,1997,207(5):721—729. [11] Anindya Chatterjee.The short-time impulse response of euler-bernoulli beams[J].ASME Journal of Applied Mechanics,2004,71(3):208—218.

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##### 出版历程
• 收稿日期:  2005-09-26
• 修回日期:  2006-03-28
• 刊出日期:  2006-07-15

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