Summary
Closed-form solutions of the dynamic response of cross-ply laminated circular cylindrical shells are developed for arbitrary boundary conditions and under arbitrary loadings. The equations of motion of the classical, first-order and third-order theories are converted into a single-order system of equations by using state variables. To solve for the dynamic response, the biorthogonality conditions of principle modes of the original and adjoint eigenfunctions are used to decouple the state space equation. The study reveals that the disagreement between shear deformation theories in much less than the disagreement between them and the classical theory.
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Khdeir, A.A. Dynamic response of cross-ply laminated circular cylindrical shells with various boundary conditions. Acta Mechanica 112, 117–134 (1995). https://doi.org/10.1007/BF01177483
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DOI: https://doi.org/10.1007/BF01177483