Wang Jin-ying, Lü Zhong-da. Transversely Isotropic Beam under Enitial Stress[J]. Applied Mathematics and Mechanics, 1990, 11(6): 537-646.
Citation: Wang Jin-ying, Lü Zhong-da. Transversely Isotropic Beam under Enitial Stress[J]. Applied Mathematics and Mechanics, 1990, 11(6): 537-646.

Transversely Isotropic Beam under Enitial Stress

  • Received Date: 1989-09-25
  • Publish Date: 1990-06-15
  • 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.
  • loading
  • [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.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1807) PDF downloads(478) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return