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粘弹性厚板的动力方程

杨正文 杨挺青

杨正文, 杨挺青. 粘弹性厚板的动力方程[J]. 应用数学和力学, 1992, 13(5): 459-467.
引用本文: 杨正文, 杨挺青. 粘弹性厚板的动力方程[J]. 应用数学和力学, 1992, 13(5): 459-467.
Yang Zheng-wen, Yang Ting-qing. An Equation of Motion for a Thick Viscoelastic Plate[J]. Applied Mathematics and Mechanics, 1992, 13(5): 459-467.
Citation: Yang Zheng-wen, Yang Ting-qing. An Equation of Motion for a Thick Viscoelastic Plate[J]. Applied Mathematics and Mechanics, 1992, 13(5): 459-467.

粘弹性厚板的动力方程

基金项目: * 国家自然科学基金资助项目

An Equation of Motion for a Thick Viscoelastic Plate

  • 摘要: 本文导出了一般粘弹性厚板含剪切、挤压和转动惯性效应的动力方程,它是弹性厚板动力方程的推广.据此方程还可退化得到若干种类型的中厚度粘弹性板的动力方程.
  • [1] Reissner,E.,The effect of transverse shear deformation on the bending of elastic plates,J.Appl.Mech.,12 (1945),69-77.
    [2] Mindlin,R.D.,Influence ofrotatory inertia and shear on flexural motions of isotropic elastic plates,J.Appl.Mech.,18 (1951),31-38.
    [3] 胡海昌,各向同性夹层板反对称小挠度的若干问题,力学学报,(6)(1963),53-60
    [4] 曹志远、杨异田,《厚板动力学理论及其应用》,科学出版社(1983).
    [5] Radovskii,B.S.,Application of the calculation scheme for a layered viscoelastic medium to the estimation of the stressed state of highways and airport pavements with moving loads,Soviet Appl.Mech.,15,10 (1979),940-946.
    [6] Hewitt,J.S.and J.Mazumdar,Vibration of viscoelastic plates under transverse load by the method of constant deflection contours,J.Sound Vib.,33,3 (1974),319-333.
    [7] Robertson,S.R.,Solving the problem of forced motion of viscoelastic plates by Valanis' method with an application to a circular plate,J.Sound Vib.,14,3 (1971),263-278.
    [8] 杨挺青等,粘弹性基支薄板的准静态弯曲,华中工学院学报,15(1987),1-6
    [9] Mase,G.E.,Behavior of viscoelastic plates inbending,J.Engng Mech.Div.ASCE,86,EM3 (1960),25-39.
    [10] Pan,H,H.,Vibration of viscoelastic plates,J.de Mecanique,5,3 (1966),355-374.
    [11] Nagaya,K.,Dynamics of viscoelastic plate with curved boundaries of arbitrary shape,J.Appl.Mech.,45 (1978),629-635.
    [12] Pister,K.S.,Viscoelastic plate on a viscoelastic foundation,J.Engng.Mech.Div.ASCE,87,EM1(1961),43-54.
    [13] Srinivas,S.and A.K.Rao,Flexure of thick rectangular viscoelastic plates,J.Engng Mech.Div.ASCE,98,EM3,(1972),771-776.
    [14] Kobayashi,H.and K.Sonoda,Thick circular plates on linear viscoelastic foundations,Proc.31rd Japan National Congress for Appl.Mech.,Tokyo,Theo.& Appl.Mech.,81,Nov.(1981),153-164.
    [15] Gurtin,M.E.and E.Sternberg,On the linear theory of viscoelasticity,Arch.Rational Mech.Anal.,11 (1962),291-356.
    [16] Власов Б.Ф.,Об уравнениях теории изгиба пластинок,Изэ.АН СССР.ОТН,12(1957),57-60
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出版历程
  • 收稿日期:  1991-05-11
  • 刊出日期:  1992-05-15

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