Energy Methods in Composite Material Shells
Many composite material structures not only involve anisotropy, multilayer considerations and transverse shear deformat mal effects, which can be very important. True, for preliminary design and analysis one often uses the simplified, easier to use analyses that have been presented earlier, but for the final design, transverse shear deformation and hygrothermal effects must be included. These thermal and moisture effects have been described in Chapter 14. Analytically they cause considerable difficulty, because with their inclusion few boundary conditions are homogeneous, hence separation of variables, used throughout the shell solutions to this point, cannot be utilized straightforwardly. Only through the laborious process of transformation of variables can separation of variables be used [See 22.1, pp. 63–66]. Therefore, energy principles are much more convenient for use in design and analyses of plate and shell structures when hygrothermal effects are present. Recently, the incorporation of piezoelectric effects, analogous to the thermal and hygrothermal effects, provides another source of nonhomogenous boundary conditions [22.2].
KeywordsComposite Material Cylindrical Shell Nonlinear Vibration Displacement Function Flexural Vibration
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- 22.1.Vinson, J. R., “The Behavior of Thin Walled Structures: Beams Plates and Shells”, Kluwer Academic Publishers, Dordrecht, 1989.Google Scholar
- 22.2.Leibowitz, M. and J. R. Vinson, “Intelligent Composites: Design and Analysis of Composite Material Structures Involving Piezoelectric Material Layers. Part A-Basic Formulation”, Center for Composite Materials Technical Report 9154, Univeristy of Delaware, November 1991.Google Scholar
- 22.4.Yamaki, N., “Dynamic Behavior of a Thin-Walled Circular Cylindrical Shell”, in “Development in Thin-Walled Structures - 1” edited by Rhodes, J. and Walked, A. C., Applied Science Publishers, London, 1982.Google Scholar
- 22.6.Olson, M. D., “Some Experimental Observations on the Nonlinear Vibration of Cylindrical Shells”, AIAA Journal (Tech. Notes), Vol. 3, pp. 1775–1777, 1965.Google Scholar
- 22.8.Chu, H. N., “Influence of Large Amplitude of Flexural Vibrations of a Thin Circular Cylindrical Shell”, Journal of Aerospace Science, Vol. 28, pp. 602609, 1961.Google Scholar
- 22.9.Evensen, D. A., “Non-linear Flexural Vibration of Thin Walled Circular Cylinder”, NASA TND-4090, 1967.Google Scholar
- 22.10.Hirano, Y. and J. R. Vinson, “Nonlinear Vibrations of Composite Material Cylindrical Shells”, Proceedings of the Fourth Japan-U.S. Conference on Composite Materials, Technomic Publishing Company, Lancaster, Pa, pp. 340–348, 1988.Google Scholar
- 22.11.Hirano, Y., “Nonlinear Vibrations of Composite Material Shells, Ph.D. Dissertation, Department of Mechanical Engineering, University of Delawarem 1988.Google Scholar
- 22.12.Sokolnikoff, I. S., “Mathematical Theory of Elasticity”, McGraw-Hill Book Company, Second Edition, 1956.Google Scholar
- 22.Nowinski, J. L., “Nonlinear Transverse Vibrations of Orthotropic Cylindrical Shells”, AIAA Journal, Vol. 1, pp. 617–620, 1963. The Behavior of Shells Composed of Isotropic and Composite Materials 471Google Scholar
- 22.14.Mickens, R. E., “An Introduction to Nonlinear Oscillations”, Cambridge University Press, Cambridge, 1981.Google Scholar
- 22.15.Leissa, A. W., “Vibration of Shells”, NASA SP-288, U. S. Government Printing Office, 1973.Google Scholar