梁-柱体系在椭圆型荷载作用下的精确解和动力屈曲分析

Exact Solution and Dynamic Buckling Analysis of a Beam-Column System Having the Elliptic Type Loading

Department of Mechanical Engineering, Izmir Institute of Technology, Gulbahce Koyu, 35430 Urla-Izmir, Turkey

摘要: 当梁-柱体系两端铰支时，在随时间周期变化的椭圆型轴向压力的作用下，给出了其动力稳定性问题的一个闭合解．采用Fourier正弦级数形式，以及解析地求解由此产生的常微分方程，求得控制方程的解．找到动力屈曲问题精确的解析解是有困难的，然而该体系的物理特性，为精确解的存在提供了充分的依据．另外，还研究了体系的频率响应特性，静力、驱动力和频率比对临界屈曲荷载的影响．
- 动力屈曲 /
- 精确解 /
- Jacobi椭圆函数 /
- 稳定-不稳定
Abstract: A closed form solution of the dynamic stability problem of a beam-column system with hinged ends loaded by an axial periodically time varying compressive force of an elliptic type was presented.Solution of the governing equation was obtained in the form of Fourier sine series and the resulting ordinary differential equation was solved analytically.Finding the exact analytical solutions of the dynamic buckling problems were difficult.However, availability of exact solutions provided adequate understanding about the physical characteristics of the system.The frequency-response characteristics of the system, the effects of static load, driving forces and frequency ratio on the critical buckling load were also investigated.
- dynamic buckling /
- exact solution /
- Jacobi elliptic functions /
- stability-instability

[1]	Bazant Z P, Cedolin L. Stability of Structures Elastic, Inelastic, Fracture, and Damage Theories[M]. Mineola, New York: Dover Publications Inc, 2003.
[2]	Dario Aristizabal Ochoa J. Static and dynamic stability of uniform shear beam-columns under generalized boundary conditions[J]. Journal of Sound and Vibration, 2007, 307(1/2): 69-88. doi: 10.1016/j.jsv.2007.06.049
[3]	Pavlovic R, Kozic P, Rajkovic P, Pavlovic I. Dynamic stability of a thin-walled beam subjected to axial loads and end moments[J]. Journal of Sound and Vibration, 2007, 301(3/5): 690-700. doi: 10.1016/j.jsv.2006.10.032
[4]	Sampaio J H B, Hundhausen J R. A mathematical model and analytical solution for buckling of inclined beam-columns[J]. Applied Mathematical Modelling, 1998, 22(6): 405-421. doi: 10.1016/S0307-904X(98)10014-8
[5]	Zuniga A E. Analysis of a beam-column system under varying axial forces of elliptic type: the exact solution of Lamé’s equation[J]. International Journal of Solids and Structures, 2004, 41(8): 2155-2163. doi: 10.1016/j.ijsolstr.2003.11.036
[6]	Abramowitz M, Stegun I A. Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables[M]. New York: Dover Publications Inc, 1965.
[7]	Polyanin A D, Zaitsev V F. Handbook of Exact Solutions for Ordinary Differential Equations[M]. USA: CRC Press, 1995.
[8]	Lawden D F. Elliptic Functions and Applications[M]. New York: Springer-Verlag, 1989.