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.
Similar content being viewed by others
References
Junger, M.C., Dynamic behavior of reinforced cylindrical shells in a vacuum and in a fluid,J. Appl. Mech., 3 (1954).
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).
Wah, T., Flexural vibrations of ring-stiffened cylindrical shells,J. Sound. Vib., 3 (1966).
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).
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.
Garnet, H., and A. Levy, Free vibtations of reinforeced elastic shells,J. Appl. Mech., 36 (1969).
Basdekas, N.L. and M. Chi, Response of oddly-stiffened circular cylindrical shell,J. Sound. Vib. 17 (1971).
Mikulas. M.M. Jr., and J.A. Mcelm, On free vibrations of eccentrically stiffened cylindrical shells and flat plates,NASA, TN-D-3010 (1965).
Hoppmann, W.H.II, Some characteristies of the flexural vibrations of orthogonally stiffened cylindrical shells,J. Acoust. Soc. Am., 30 (1958).
Patel. J.S., Natural frequencies and strain distribution in a ring-stiffened thick cylindrical shell.J. Acoust. Soc. Am., 47 (1970).
Dai Shi-qiang, The method of PLK,The Theory and Application in Mechanics of Singular Perturbation, Edited by Chien Wei-zang, Science press (1981). (in Chinese)
Li Long-yuan, Stability and vibration analyses of arbitrary varying thickness plates,Shanghai Mechanics (1986). (in Chinese)
Li Long-yuan, Vibration analysis of moderate-thick plates with slowly varying thickness,Appl. Math. and Mech. 7, 7 (1986), 655–662.
Flugge, W.,Stress in Shell, Springer-Verlag, (1960).
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.
Author information
Authors and Affiliations
Additional information
Communicated by Pan Li-zhou
Rights and permissions
About this article
Cite this article
Long-yuan, L. A perturbation solution of free vibration of cylindrical shells with ring-stiffeners. Appl Math Mech 8, 283–292 (1987). https://doi.org/10.1007/BF02018554
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02018554