弹性直杆中一类动力屈曲问题的渐近解

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基金项目: 国家自然科学基金;山西省自然科学基金

The Asymptotic Solution of a Dynamic Buckling Problem in Elastic Columns

1.
Department of Mechanics, College of Traffic and Communications, South China University of Technology, Guangzhou 510641, P. R. China;
2.
Taiyuan University of Technology, Taiyuan 030024, P. R. China

摘要: 对于弹性杆受刚性块轴向撞击的动力屈曲问题而言,由于轴向载荷形式较为复杂,问题将归结为关于非线性偏微分方程组解的讨论,至今仍未能得到一个理论上的解析解,为此,讨论了有限长理想弹性直杆的此类动力屈曲问题,采用小参数的摄动展开和变分法,成功地得到了这一问题的一个理论上的近似解,并给出了相应的算例,从中得到了一些有益的结论.
- 动力屈曲 /
- 摄动法 /
- 屈曲模态
Abstract: For the dynamic buckling of an elastic column, which is subjected to a longitudinal impact by a rigid body, the form of the axial load is very complicated. The problem may be reduced to discuss the solution of nonlinear partial differential equations. So far, a theoretical solution may not be obtained. In this paper, this dynamic buckling problem of an ideal elastic column with finite length is discussed. By the perturbation method with a small parameter and the variational method, a solution of this problem is given. Finally, numerical computation is carried out, from this, some beneficial.
- dynamic buckling /
- perturbation method /
- buckling mode

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