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The nonlinear analysis and computation on horizontal catenary midpoint under concentrating force

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 作者 单位 E-mail 郭小刚 湘潭大学土木工程与力学学院 teenhero@163.com 周涛 湘潭大学土木工程与力学学院 zhoutao20080602@126.com 金星 长沙矿冶研究院、深海矿产资源开发利用技术国家重点实验室 邓旭辉 湘潭大学土木工程与力学学院

本文首先对均布力作用下悬链线理论进行了深入的分析研究，推导出求解水平张力单参数和双参数形式的隐含超越方程，在算法上验证了两种方程的等价性。关于悬链线固有的广义倾角、曲率半径、约束反力和水平张力的嵌入关系等给出了具有新意的表达公式。然后建立了水平悬链线在对称集中力作用下的平衡方程，对于不同垂向集中力作用下水平张力的变化情况和最大垂直距离差所在水平位置随集中力的变化等进行了非线性计算。本文提出的理论构建和分析具有创新性，在理论探索和工程应用上具有重要意义。

At first this article has carried on the thorough research on the catenary theory, and the implicit transcendental equations of single and double parameter to solve the horizontal tension are deduced, verifying the equivalence of two transcendental equations by algorithm. Intrinsic generalized angle, radius of curvature, constraint forces of the catenary as well as the embedded relation of relative horizontal tension are presented with new conception. Besides, the equilibrium equation of horizontal catenary under the symmetric concentrating force is established, the analysis on unknown vertical distance is presented, the paper have computed the nonlinear variation of horizontal location and maximum of vertical distance difference with concentrating force and the change situation of horizontal tension under the effect of different downward concentrating forces. The theory-building and analysis presented here have primitive innovation, which is of great significance in the engineering and in theoretical exploration.
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