关于具有初始挠度的圆薄板的跳跃问题
On The Jumping Problems of A Circular Thin Plate With Initial Deflection
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摘要: 本文利用江福汝提出的“两变量法”[3][4]与正则摄动法研究了具有初始挠度的圆薄板的跳跃问题[本文中(1.1),(1.2)]。我们得到了这一问题的N阶一致有效渐近解[(1.66),(1.67)]。当初始挠度变为零时,该解变为圆薄板非线性弯曲问题的解[6];如果初始挠度较大而初始挠度与载荷强度符号相反时,载荷强度达到某一值时,将发生跳跃现象。Abstract: In this paper, the jumping problems of a circular thin plate with initial deflection are studied by using the method of two variables,[3][4]proposed by Jiang Fu-ru and the method of the normal perturbation (in this paper (1.1), (1.2)). We obtain Nth-order uniformly valid asymptotic expansion of the solution of this problem ((1.66), (1.67)). When the initial deflection vanishes the solution of a circular thinplate with initial deflection is reduced to the solution of the problems of the nonlinear bending of a circular thin plate [6]. If the initial deflection is largish and the signs of the initial deflection with the intensity of the transverse load are opposite, when the intensity of the transverse load reaches a certain value, the circular thin plate with initial deflection should produce the Jumping phenomenon[8].
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[1] Chien Wei-zang, Asymptotic behavior of a thin clamped circular plate under uniform normal pressure at very large deflection, Sci. Rep.Nai.Tsinghua Univ.Ser.,A, 5(1948, 71-94. [2] 江福汝,环形和圆形薄板在各种支承条件下的非对称弯曲问题(Ⅰ),应用数学和力学,3,5(1982), 629-640. [3] 江福汝,环形和圆形薄板在各种支承条件下的非对称弯曲问题(Ⅱ),应用数学和力学,5,2(I984), 191-202. [4] 江福汝,摄动方法在薄板弯曲问题中的某些应用,应用数学和力学,1, 1 (1980), 37-53. [5] 秦圣立、张爱淑,关于环形薄板的屈曲问题,应用数学和力学,8, 2 (1985), 175-190. [6] 秦圣立、张爱淑、康连成,关于圆形薄板的轴对称非线性弯曲问题,第一届华东固体力学学术讨论会论文集,(1984). [7] R. E.奥写利,《奇异摄动引论》,科学出版社(1983), 24-30. [8] A. C.沃耳密尔,《柔粗板与柔粗壳》,科学出版社〔1959),162-193. -
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