闭口薄壁杆件受碰撞的振动方程求解

罗旗帜; 徐中山; 陈玉骥

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闭口薄壁杆件受碰撞的振动方程求解

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- 闭口薄壁杆件受碰撞的振动方程求解
- Solution of Dynamic Equation in Thin-Walled Close Section Beam under Impact
- 中北大学学报（自然科学版） 2010年31卷第4期页码：348-351
- 作者机构：
  
  1. 佛山科学技术学院土木工程与建筑学系
  2. 华南理工大学土木与交通学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(50978058);全国优秀博士学位论文作者专项基金资助项目(200954)
- DOI：
  中图分类号：
- 纸质出版：2010
- 稿件说明：
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罗旗帜, 徐中山, 陈玉骥. 闭口薄壁杆件受碰撞的振动方程求解[J]. 中北大学学报（自然科学版）, 2010,31(4):348-351.

罗旗帜, 徐中山, 陈玉骥. Solution of Dynamic Equation in Thin-Walled Close Section Beam under Impact[J]. 2010, 31(4): 348-351.
罗旗帜, 徐中山, 陈玉骥. 闭口薄壁杆件受碰撞的振动方程求解[J]. 中北大学学报（自然科学版）, 2010,31(4):348-351. DOI：

罗旗帜, 徐中山, 陈玉骥. Solution of Dynamic Equation in Thin-Walled Close Section Beam under Impact[J]. 2010, 31(4): 348-351. DOI：

摘要

基于薄壁杆件理论、能量泛函变分原理和闭口薄壁杆件翘曲函数的特征

推导了闭口薄壁杆件的双向弯扭耦合动力方程

此方程可退化为Bernoulli-Euler梁弯扭耦合动力方程.根据结构的边界条件、连续条件和碰撞接触平衡条件

采用Laplace积分变换和逆变换方法求解闭口薄壁杆件受碰撞的动力方程

获得了闭口薄壁杆件的各种瞬态动力响应.将结果与Bernoulii-Eurler薄壁梁理论结果相比较

计算结果表明:考虑剪切变形对冲击力和扭转角的影响不大

但对位移的影响比较显著.

Abstract

The dynamic differential equations of coupled bending and torsional vibration in Timoshenko thin-walled beam with closed section had been deduced based on the theory of thin-walled structures

the dynamic differential equations and the characteristic of warping function.The equations can be degenerated into the differential equation of coupled bending and torsional vibration in Bernoulli-Euler thin-walled beam with closed section.Then

according to boundary conditions

continuous condition and impact contact equilibrium condition

the dynamic differential equations in thin-walled closed section beam under impact were solved by Laplace transform and inverse transform

and all kinds of transient dynamic responses of beam have been obtained.Finally

the result was compared with the result which was solved based on the theory of BernoulliEuler thin-walled beams.It shows that shear deformation has little effect on impact force and torsion angle

but has much effect on displacement.

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Keywords

references

Lam K Y,Sathiyamoorthy T S.Reponse of composite beam under low-velocity impact of multiple masses[J].Compsite Structures,1999,44:205-220.

Yang J L,Xi F.Experimental and theoretical study of free-free beam subjected to impact at any cross-section alongits span[J].International Journal of Impact Engineering,2003,28:761-781.

黄剑敏,任文敏.弹性杆与结构接触冲击的冲击力计算研究[J].应用力学学报,1996,13(3):115-118.Huang Jianmin,Ren Wenmin.Impact force calculative investigation of contact impact between elastic bar andstructure[J].Chinese Journal of Applied Mechanics,1996,13(3):115-118.(in Chinese)

鲍四元,邓子辰.弹性撞击作用下弯扭耦合梁的动力响应[J].应用力学学报,2008,25(3):415-420.Bao Siyuan,Deng Zichen.Dynamic response of bending-torsion coupled beam under elastic impact[J].ChineseJournal of Applied Mechanics,2008,25(3):415-420.(in Chinese)

李俊,金咸定,何东明.确定性荷载作用下Timoshenko薄壁梁的弯扭耦合动力响应[J].力学季刊,2002,23(3):380-385.Li Jun,Jin Xianding,He Dongming.Dynamic response of bending-torsion coupled timoshenko thin-walled beamunder deterministic loads[J].Chinese Quarterly of Mechanics,2002,23(3):380-385.(in Chinese)

包世华,周坚.薄壁杆件结构力学[M].北京:中国建筑工业出版社,2006.

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