力学与实践 ›› 2020, Vol. 42 ›› Issue (5): 594-597.DOI: 10.6052/1000-0879-20-015

• 应用研究 • 上一篇    下一篇

四类变截面悬臂梁在侧向三角形载荷下的挠度1)

廖晗, 姜吕锋, 李恒达, 杨兴昌, 李映辉2)   

  1. 西南交通大学力学与工程学院, 成都 610031
  • 收稿日期:2020-01-14 修回日期:2020-03-11 出版日期:2020-10-08 发布日期:2020-10-22
  • 通讯作者: 2) E-mail: yinghui.li@swjtu.edu.cn
  • 基金资助:
    1) 国家自然科学基金(11872319)和西南交通大学SRTP项目(201910613068)资助

DEFLECTION OF FOUR TYPES OF CANTILEVER BEAMS WITH VARIABLE CROSS SECTION UNDER LATERAL TRIANGULAR DISTRIBUTED LOADS1)

LIAO Han, JIANG Lüfeng, LI Hengda, YANG Xingchang, LI Yinghui2)   

  1. School of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China
  • Received:2020-01-14 Revised:2020-03-11 Online:2020-10-08 Published:2020-10-22

摘要: 研究了圆柱、圆锥、抛物型和双曲型回转变截面悬臂梁在侧向三角形分布载荷下的挠度。基于四类回转悬臂梁的惯性矩沿长度方向的分布规律,得到其任意侧向分布载荷下的挠曲线方程。基于三角形分布载荷下的挠曲线方程,得到其端部挠度值。在等长度和等体积假设下,通过比较端部挠度值找到四类悬臂梁中挠度最小者。研究表明三角形分布载荷下,特征参数在特定范围内,母线为双曲线的悬臂梁挠度最小。

关键词: 悬臂结构, 回转型梁, 弯曲变形

Abstract: The deflection of cylindrical, conical, parabolic and hyperbolic cantilever beams with reversed sections under laterally triangular distributed loads is studied. Firstly, from the distribution of moment of inertia along the length direction of four types of rotating cantilever beams, the deflection curve equation under any lateral triangular distributed load is obtained. Based on the deflection curve equation under the linear load, the deflection at the lower end of the lateral triangular distributed load is obtained. Under the assumption of equal length and equal volume, the minimum deflection among the four types of cantilever beams is found by comparing the end deflection values. It is shown that among the four types of cantilever beams under lateral triangular distributed load, the characteristic parameters are within a specific range, and the deflection of the cantilever beam with hyperbolic bus is the smallest.

Key words: cantilever structure, revolving beam, bending deformation

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