初始应力作用下的横向各向同性梁

王晋莹; 吕忠达

初始应力作用下的横向各向同性梁

西安公路学院

计量
- 文章访问数: 1808
- HTML全文浏览量: 76
- PDF下载量: 478
- 被引次数: 0
出版历程
- 收稿日期: 1989-09-25
- 刊出日期: 1990-06-15

Transversely Isotropic Beam under Enitial Stress

Xi'an Highway Institute, Xi'an

摘要

摘要: 本文从Novozhilov的非线性弹性理论基本方程出发,经适当的简化,用沿梁横截面积分的方法导出任意非均匀初始应力场作用下的横向各向同性梁的运动方程.当初始应力不存在时,方程退化为经典的Timoshenk0梁方程,作为例子,本文用所得的方程,研究了在初始轴向力、初始弯矩作用下的横向各向同性梁的屈曲及振动特性.

Abstract: Starling from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.

HTML全文

参考文献(13)

[1]	Biot,M.A.,Nonlinear theory of elasticity and the linearized case for a body under initial stress,Phil.Mag.,27(1940),468-489.
[2]	Biot.M.A.,Increases of torsional stiffness of a prismatical bar due to axial tension,J.Applied Physics,10(1939),860-864.
[3]	Herrmann,G.and A.E.Armenakas,Vibrations and stability of plates under initial stress Trans.ASCE,127,Part 1(1962),458-487.
[4]	Brunelle.E.J.,The statics and dynamics of a transversely isotropic Timoshenko beam,J.Composite Materials,4(1970),404-416.
[5]	Novozhilov,V.V.,Foundations of the Nonlinear Theory of Elasticity,Graylock Press Rocheter.N.Y.(1953).
[6]	Bolotin,V.V.,Non-Conservative Problems of the Theory of Elastic Stability,Macmillan,New York(1963).
[7]	Mindlin,R.D.and H.Deresiewicz,Timoshenko's shear coefficient for flexural vibrations of beams,Proc.of the 2nd U.S.National Congress of Applied Mechanics.(1954),175.
[8]	Wang,J.Y.and N.G.Stephen,Effect of initial stress on vibration and buckling of a Timoshenko beam.Proc.of ICMDEA(1988).
[9]	Cowper.G.R.,The shear coefficient in Timoshenko's beam theory,Trans.ASME.J.Appl.Mech.,33(1966),335-340.
[10]	Sokolnikoff,I.S.,Mathematical Theory of Elasticity,2nd Edition,McGraw-Hill Book Company,Inc.,New York,N.Y.(1956).
[11]	Timoshenko,S.and D.H.Young,Vibration Problems in Engineering,4th Edition,John Wiley & Sons(1974).
[12]	Levison,M.,Free vibrations of a simply supported rectangular plate:an exact elasticity solution,J.Sound and Vibration,98,2(1985),289-298.
[13]	Stephen,N.G.,The second frequency spectrum of Timoshenko beams,J.Sound and Vibration,80(1982),578-582.