全部

力学与实践 ›› 2020, Vol. 42 ›› Issue (1): 85-91.doi: 10.6052/1000-0879-19-176

• 教育研究 • 上一篇    下一篇

有限到无限:基于离散静力平衡推导悬链线方程和梁位移方程

罗雯瑛1)   

  1. 清华大学航天航空学院,北京 100084
  • 收稿日期:2019-05-05 发布日期:2020-03-13
  • 通讯作者: 1) 罗雯瑛,清华大学航天航空学院2017级本科生。E-mail: luowy17@mails.tsinghua.edu.cn

FROM FINITENESS TO INFINITY: DERIVING THE CATENARY EQUATION AND THE BEAM DISPLACEMENT EQUATION BASED ON THE DISCRETE STATIC EQUILIBRIUM MODEL

LUO Wenying1)   

  1. School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
  • Received:2019-05-05 Published:2020-03-13

摘要: 悬链线问题是一类非常经典的力学问题,推导出悬链线方程的方法从静力平衡到变分原理,非常之多。本文基于离散的静力平衡模型,采用从有限到无限的求解方法,建立并求解了悬链线方程。在此基础上,本文进一步建立了含有扭簧作用的离散静力平衡模型,推导并求解梁位移方程。最后在不同参数下求解梁位移方程得到其渐变解,并分析了多种平衡状态的存在情况。

关键词: 静力平衡, 悬链线,

Abstract: The catenary problem is a very classical mechanical problem. There are many methods to derive the catenary equation from static equilibrium methods to variational principles. This paper establishes and solves the catenary equation based on the discrete static equilibrium model. Furthermore, this paper establishes a discrete static equilibrium model with torsion spring, then derives and solves the beam displacement equation. In the end, the beam displacement equations with different parameters are solved to obtain the gradual solution, and the existence of various equilibrium states is analyzed.

Key words: static equilibrium, catenary curve, beam

中图分类号: 

  • O312