Vibrations of Fiber-Reinforced Laminated Deep Shells

Abstract

This paper deals with a numerical method for the free vibrational analysis of laminated deep shells. The strain-displacement relations are obtained for a general laminated shell geometry described by orthogonal curvilinear coordinates. Parabolic variation of transverse shear stresses along the thickness and the effects of rotary inertia are included in the formulation. The displacement fields are represented by Bezier patches. The shape and size of these patches are controlled by certain arbitrary points called control points. Owing to the special characteristics of these control points, the treatment of displacements, slopes, curvatures, etc., at a particular edge becomes very simple. Hence, the enforcement of boundary conditions along the edges is straightforward. Ritz-type solution procedure is used for the eigen-analysis of the shell structure. Numerical examples involving laminated spherical, conical, and cylindrical shells are investigated in detail. Such shell geometries usually have planes of symmetry; hence, only one-quarter of the shell is analyzed in this study. Good convergence of the natural frequencies is observed by using eighth-order Bezier functions. The results are compared with the existing sources in the literature. The influences of material strength and number of layers on the natural frequencies are also examined.