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| Nonlinear analysis and computation on horizontal catenary midpoint under concentrating force |
| Received:March 04, 2017 Revised:June 07, 2017 |
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| DOI：10.7511/jslx20170304001 |
| KeyWord:catenary vertical concentrating force horizontal tension equilibrium equation nonlinear computation |
| Author | Institution |
| 郭小刚 |
湘潭大学 土木工程与力学学院, 湘潭 ;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, 长沙 |
| 周涛 |
湘潭大学 土木工程与力学学院, 湘潭 |
| 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, 长沙 |
| 邓旭辉 |
湘潭大学 土木工程与力学学院, 湘潭 |
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| Abstract: |
| At first this article carries out thorough research on the catenary theory,derives the implicit transcendental equations with a single parameter and with double parameters for the horizontal tension, and proves the equivalence of two transcendental equations by algorithm.New mathematical formulas for the intrinsic generalized angle,radius of curvature,constraint forces of the catenary as well as the embedded relation of relative horizontal tension are presented.Besides,the equilibrium equation of horizontal catenary under the symmetric concentrating force is established,and the unknown vertical distance is determined.The paper calculates the nonlinear variation of horizontal tension and maximum of vertical distance with concentrated force location.The theory-and analysis presented are novel,which is of great significance in the engineering and in theoretical exploration. |
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