| 受圆柱面约束弹性杆的平衡与稳定性 |
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| 引用本文： | 刘延柱,薛纭.受圆柱面约束弹性杆的平衡与稳定性[J].应用力学学报,2005,22(3):391-394. |
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| 作者姓名： | 刘延柱 薛纭 |
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| 作者单位： | 1. 上海交通大学,上海,200030
2. 上海应用技术学院,上海,200233 |
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| 基金项目： | 国家自然科学基金(No.10472067) |
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| 摘 要： | 讨论受圆柱面约束的圆截面弹性杆的平衡与稳定性。以描述截面姿态的欧拉角为变量,建立受约束弹性杆的平衡方程。利用方程的初积分导出约束力、截面内力及挠性线的解析表达式。作为特殊的平衡状态,讨论杆的螺旋线平衡的存在条件。用相平面法分析螺旋线平衡的稳定性,导出解析形式的稳定性条件。
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| 关 键 词： | 弹性细杆 圆柱面约束 稳定性 相平面法 |
| 文章编号： | 1000-4939（2005）03-0391-04 |
| 收稿时间： | 2004-08-01 |
| 修稿时间： | 2004-08-012005-01-18 |
Equilibrium and Stability of Elastic Rod Constrained to Cylinder |
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| Liu Yanzhu,Xue Yun.Equilibrium and Stability of Elastic Rod Constrained to Cylinder[J].Chinese Journal of Applied Mechanics,2005,22(3):391-394. |
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| Authors: | Liu Yanzhu Xue Yun |
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| Abstract: | The equilibrium and stability of an elastic rod with circular cross section under the constraint of a cylinder is discussed.The differential equations of equilibrium of the constrained rod are established taking Euler angles as variables to describe the attitude of the cross section.The analytical expressions of constraint force,internal force on cross section,and flexibility of the rod are obtained via the first integrals.The existence conditions of helical equilibrium are discussed as a special configuration of the rod.The stability of the helical equilibrium is analyzed with phase plane method,and an analytical criterion of stability is revealed. |
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| Keywords: | thin elastic rod cylinder constraint stability phase plane method |
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