EI、Scopus 收录

 引用本文: 胡海昌 钟万勰. 考虑剪应变的弹性薄壁杆件的振动理论[J]. 力学学报, 1957, 1(2): 193-204.
Haichang Hu, Wanxie Zhong. THE EFFECT OF SHEAR DEFORMATION ON THE VIBRATIONS OF ELASTIC THIN WALLED BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1957, 1(2): 193-204.
 Citation: Haichang Hu, Wanxie Zhong. THE EFFECT OF SHEAR DEFORMATION ON THE VIBRATIONS OF ELASTIC THIN WALLED BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1957, 1(2): 193-204.

## THE EFFECT OF SHEAR DEFORMATION ON THE VIBRATIONS OF ELASTIC THIN WALLED BEAMS

• 摘要: 对于开口截面彈性薄壁杆件的振动問題,符拉索夫在1940年提出的理論,是基于下列两个基本假設:(1)截面具有剛硬不可变形的周綫;(2)中曲面无剪应变。其后,有些学者也曾提出过相同的理論(例如.R.海里格).由于忽略了中曲面的剪应变,我們可以估計得到,符拉索夫的理論只适用于研究低频率的固有振动和強迫振动,而不适用于研究高频瘁的振动。由于行动載荷和冲击载荷必然引起各个固有频率的振动,因此符拉索夫的理論也不适用于研究这些載荷作用下的振动問題。为了要更好地研究这些問題,必須要考慮剪应变的影响。

Abstract: In this paper, a theory is proposed for the vibrations of elastic thin walled beams of open cross sections, where the effect of shear deformation is approximately taken into account. The theory is based on the following assumptions:1) The transverse cross section of the beam is rigid. Therefore its motion may be defined by the deflections ξ(z,t), η(z,t) and the angle of torsion θ(z,t) about the center of twist.(2) The longitudinal displacement ω(z,8,t)and the longitudiual normal stress σ(z,8,t) have the following four torms expression:3) The mean value of the shcaring stress across the thickness of beam has the following three terms expression:4) The effect of non-uniform shearing stress distribution may be counted for by introducing a twisting moment:Then the stress deformation relations, equations of motion, and boundary conditions are derived from a variational principle of reference 4, The final equations are Eqs. (24), (26), (21).In the case of beams having two planes of symmetr...

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈