Vibration of Isotropic Shells

  • Jack R. Vinson
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 18)


Entire texts are needed to discuss shell vibrations in their entirety. In this Chapter, axially symmetric vibrations are discussed first so that through their simplicity, it is easy to see how static equations are easily transformed to dynamic equations, and to show the relation to the vibrations of beams: with and without an elastic foundation. Next, the general vibration characteristic of shells are shown through the study of cylindrical shells, also relating the behavior to beam vibrations. Through the work of Koga, only five types of boundary conditions are needed to study any and all boundary conditions. Next, the time portion of dynamic loads is presented in an easy to use manner to study impact response of shells. Finally, the important areas of shells vibrating in beam modes is studied, using two different approaches. This chapter and the references given provide a background for further study of shell vibrations. In Chapter 21, the vibrations of composite shells is discussed and could be studied upon completing this Chapter.


Cylindrical Shell Mode Shape Elastic Foundation AIAA Journal Circular Cylindrical Shell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 12.
    Thomson, W. H.,“Vibration Theory and Applications”, Prentice-Hall.Google Scholar
  2. 12.2.
    Leissa, A. W., “Vibration of Shells”, NASA SP- 288, U.S. Government Printing Office, 1973.Google Scholar
  3. 12.3.
    Koga, T., “Free Vibrations of Circular Cylindrical Shells”, JSME International Journal, Series I, Vol. 32, No. 3, 1989, pp. 311–319.Google Scholar
  4. 12.4.
    Koga, T., “Minimum Natural Frequency and Vibration Characteristics of Circular Cylindrical Shells”, Transactions of the Japan Society of Mechanical Engineers, Vol. 46, No. 411, 1980, p. 1280.CrossRefGoogle Scholar
  5. 12.5.
    Koga, T., Y. Kimpara, and A. Saito, “Inextensional Free Vibrations of Circular Cylindrical Shells, Proceedings of the JSASS/JSME Structures Conference, 1986, p. 166.Google Scholar
  6. 12.6.
    Koga, T. and A. Saito, “Inextensional Free Vibrations of Circular Cylindrical Shells”, AIAA Journal, Vol. 26, No. 12, 1988, pp. 1499–1505.MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 12.7.
    Arnold, R. N. and G. Warburton, “Flexural Vibrations of the Walls of Thin Cylindrical Shells Having Freely Supported Ends”, Proceedings of the Royal Society of London, Sec. A., Vol. 197, No. 1049, June 1949, pp. 238–256.zbMATHGoogle Scholar
  8. 12.
    Forsberg, K., “Influence of Boundary Conditions on the Model Characteristics of Thin Cylindrical Shells”, AIAA Journal, Vol. 2, December 1964, pp. 21502157.Google Scholar
  9. 12.9.
    Forsberg, K., “Axisymmetric and Beam-Type Vibrations of Thin Cylindrical Shells”, AIAA Journal, Vol. 7, February, 1969, pp. 221–227.Google Scholar
  10. 12.10.
    Koga, T., “Effects of Boundry Conditions on the Free Vibrations of Circular Cylindrical Shells”, AIAA Journal, Vol. 26, No. 11, November, 1988, pp. 1387–1394.Google Scholar
  11. 12.
    Forsberg, K., “A Review of Analytical Methods Used to Determine the Modal Characteristics of Cylindrical Shells”, NASA Contract Report 613.Google Scholar
  12. 12.13.
    Vinson, J. R. and R. L. Sierakowski, “The Behavior of Structures Composed of Composite Matrials”, Martinus-Nijhoff Publishers (now Kluwer Academic Publishers) Dordrecht, 1986.Google Scholar
  13. 12.14.
    Soler, A. I. and M. A. Brull, “An Approximate Method for the Determination of the Fundamental Bending Frequency of a Missile”, Dyna/Structures Report No. 61-A-009, October 1961.Google Scholar
  14. 12.15.
    Kingsbury, H. B. and R. E. Sennett III, “On the Free Vibrations of a Typical Solid Propellant Motor Nozzle”, Dyna/Structures, Int. Report No. 62-A-020, April 1962.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Jack R. Vinson
    • 1
  1. 1.Department of Mechanical Engineering and the Center for Composite MaterialsUniversity of DelawareNewarkUSA

Personalised recommendations