An Analytical Solution to Free Vibration Problems of Cross-ply Laminated Thin Doubly-curved Shellsby Humayun R. H. Kabir, Engineering Mechanics Research, Troy, United States,
Abstract: Hitherto an unavailable analytical solution to the free vibration boundary value problems (b.v.ps.) of symmetric and antisymmetric cross-ply laminated thin doubly-curved shells of rectangular planform is presented. Sanders' kinematic relations that incorporate Classical Lamination Theory (Kirchhoff's theory) are considered into the formulation of shell theory. The thin shell is represented by three highly coupled fourth-order partial differential equations (P.d.es.) in terms of three unknowns. A novel solution methodology based on double Fourier series approach is developed to solve these P.d.es. for SS2 type Simply Supported Boundary Conditions (S.S.B.Cs.) at all four edges. Numerical results presented herein for various parametric effects including convergence should serve as baseline solutions for future comparison of such highly popular approximate numerical techniques as, e.g., finite element and finite difference methods.
Subject Headings: Vibration | Laminated materials | Symmetry | Curvature | Finite element method | Boundary value problem | Kinematics
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