Vibration of Isotropic Shells
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.
KeywordsCylindrical Shell Mode Shape Elastic Foundation AIAA Journal Circular Cylindrical Shell
Unable to display preview. Download preview PDF.
- 12.Thomson, W. H.,“Vibration Theory and Applications”, Prentice-Hall.Google Scholar
- 12.2.Leissa, A. W., “Vibration of Shells”, NASA SP- 288, U.S. Government Printing Office, 1973.Google Scholar
- 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
- 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
- 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
- 12.9.Forsberg, K., “Axisymmetric and Beam-Type Vibrations of Thin Cylindrical Shells”, AIAA Journal, Vol. 7, February, 1969, pp. 221–227.Google Scholar
- 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
- 12.Forsberg, K., “A Review of Analytical Methods Used to Determine the Modal Characteristics of Cylindrical Shells”, NASA Contract Report 613.Google Scholar
- 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
- 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
- 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