环向加筋圆柱壳自由振动的摄动解

李龙元

环向加筋圆柱壳自由振动的摄动解

李龙元

上海市应用数学和力学研究所

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出版历程
- 收稿日期: 1986-02-05
- 刊出日期: 1987-03-15

A Perturbation Solution of Free Vibration of Cylindrical Shells with Ring-Stiffeners

Li Long-yuan

Shanghai Institute of Appl. Math, and Mech., Shanghai

摘要

摘要: 本文采用奇异摄动中的PLK方法和作者在[13]中所提出的广义Hale定理,讨论研究了带有环向加强肋圆柱壳的自由振动,由此并给出了一个计算环向加筋圆柱壳固有频率的一般计算表达式。为了验证本文解的精确性,文中还采用数值方法对此作了对比,比较结果表明,摄动一阶近似解已达到较好的精度。

Abstract: In this paper, the free vibration of cylindrical sheel with ring-stiffeners is studied in detail by using the PLK method in singular perturbation and the general Hale's law, and the formulas calculating natural frequencies of cylindrical sheel with ring-stiffeners are expressed. Finally, the FEM solution is also given to prove the perturbation solution to be seemly, and this comparison shows that the method yields very good results.

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参考文献(15)

[1]	Junger, M.C., Dynamic behavior of reinforced cylindrical shells in a vacuum and in a fluid, J.Appl.Mech., 3(1954).
[2]	Galletly, G.D., On the in-vacuo vibrations of simple supported ring-stiffened cylindrical shell, Proc.of the Second U.S.National Congress of Applied Mechanics(1954).
[3]	Wah, T., Flexural vibrations of ring-stiffened cylindrical shells, J Sound.Vib., 3(1966).
[4]	Henshell, R.D., B.K.Neale and G.B.Warburton, The natural frequencies of a complex cylindrical shell structures, Applications of Experimental and Theoritical Structural Dynamics 1(1972).
[5]	Li Long-yuan and Lu Wen-da, Analyses of free vibration and response to turbulent wind of hyperbolic cooling towers with ring stiffeners, Part I, Theoretical Analyses of Ring, IASS, Japan(1986), 9.
[6]	Garnet, H., and A.Levy, Free vibtations of reinforeced elastic shells, J Appl.Mech., 36(1969).
[7]	Basdekas, N.L.and M.Chi, Response of oddly-stiffened circular cylindrical shell, J.Sound.Vib.17(1971).
[8]	Mikulas.M.M.Jr., and J.A.Mcelm, On free vibrations of eccentrically stiffened cylindrical shells and flat plates, NASA, TN-D-3010(1965).
[9]	Hoppmann, W.H.Ⅱ, Some characteristies of the flexural vibrations of orthogonally stiffened eylindrical shells, J Acoust.Soc.Am., 30(1958).
[10]	Patel.J.S., Natural frequencies and strain distribution in a ring-stiffened thick cylindrical shell.J.Acoust.Soc.Am., 47(1970).
[11]	戴世强,PIK方法,《奇异摄动理论及其在力学中的应用》(钱伟民主编),科学出版社(1981).
[12]	李龙元,任意变厚度薄板的自由振动及稳定性分析,上海力学,2 (1986),
[13]	李龙元,缓变厚度中厚板的自由振动,应用数学和力学,7, 7 (1986), 655-662
[14]	Flügge, W., Stress in Shell, Springer-Verlag, (1960).
[15]	Li long-yuan and Lu Wen-da, Analyses of free vibration and response to turbulent wind of hyperboli cooling towers with stiffeners, Part Ⅱ:Numerical Analyses of Shell, IASS, Japan (1986), 9．