Flexural mode, thickness-shear mode and thickness-twist mode frequencies of laminated composite shells of double curvature

Abstract

The availability of limited literature on thickness-shear mode and thickness-twist mode frequencies of laminated composite plates and shells of double curvature motivated the authors to perform this research study. Cylindrical, spherical, hyperbolic paraboloid and elliptical paraboloid laminated composite shells are analyzed using a generalized higher-order shell theory. Governing equations of motion corresponding to the present theory are derived within the framework of Hamilton’s principle. Analytical solutions are obtained using Navier’s technique for the simply supported boundary conditions. Non-dimensional flexural mode, thickness-shear mode, and thickness-twist mode natural frequencies are presented. Natural frequencies obtained using the classical, first-order, and the present higher-order shell theories are compared with each other and previously published results wherever possible to verify the accuracy and efficiency of the present generalized shell theory. Thickness-shear mode and thickness-twist mode frequencies presented in this paper can be considered as one of the important contributions towards the research in dynamic analysis of laminated composite shells of double curvature.