An exact solution procedure is presented for solving free vibration problems for laminated composite noncircular cylindrical shells. Based on the classical lamination theory, strain energy and kinetic energy functional are first derived for shells having arbitrary layer stacking sequences. These functional are useful for a general analysis based upon energy principles. However, in the present work equations of motion and boundary conditions are obtained from the minimum conditions of the Lagrangian (Hamilton’s principle). The equations of motion are solved exactly by using a power series expansion for symmetrically laminated, cross-ply shells having both ends freely supported. Frequencies are presented for a set of elliptical cylindrical shells, and the effects of various parameters upon them are discussed.
Free Vibrations of Laminated Composite Noncircular Thin Cylindrical Shells
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Suzuki, K., Shikanai, G., and Leissa, A. W. (December 1, 1994). "Free Vibrations of Laminated Composite Noncircular Thin Cylindrical Shells." ASME. J. Appl. Mech. December 1994; 61(4): 861–871. https://doi.org/10.1115/1.2901569
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