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．Abstract: The objective is to present analytical solutions of longitudinal impact analysis for slender conical rods struck by a particle and a new method is proposed for conical rod-particle impact analysis, in which the superposition method is used and the response of the rod is presented. These analytical results are exact and can be used to validate the numerical methods or other analytical results. The numerical example shows that one of the advantages of the present method is that the analytical form is very simple. The result is that mass ratio and some variables describing the geometrical shape of rods such as taper, length and radius play an important role in impact dynamic system.
-
Key words:
- conical rod /
- longitudinal impact /
- mode shape /
- superposition method
-
[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. doi: 10.1006/jsvi.2000.3200 [4] HU Bin,Eberhard Peter.Symbolic computation of longitudinal impact wave[J].Comput Methods Appl Mech Engrg,2001,190(3):4805—4815. doi: 10.1016/S0045-7825(00)00348-0 [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. doi: 10.1016/S0021-8928(01)00048-X [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. doi: 10.1016/S0045-7825(97)00296-X [9] Abrate S.Vibration of non-uniform rods and beams[J].Journal of Sound and Vibration,1995,185(4):703—786. doi: 10.1006/jsvi.1995.0410 [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. doi: 10.1006/jsvi.1997.1146 [11] Anindya Chatterjee.The short-time impulse response of euler-bernoulli beams[J].ASME Journal of Applied Mechanics,2004,71(3):208—218. doi: 10.1115/1.1667531 -
计量
- 文章访问数: 2628
- HTML全文浏览量: 105
- PDF下载量: 727
- 被引次数: 0
下载:
渝公网安备50010802005915号