A Layer-Wise Analysis for Free Vibrations of Thick Composite Spherical Panels

The authors have previously presented layer-wise models for modeling the vibrations of thick composite cylindrical shells. The layer-wise theory is needed to overcome the deficiencies of conventional shear-deformable plate theories because the gradients of the deformation field are not necessarily continuous through the thickness, due to the discontinuity of material properties at layer interfaces. Fully three-dimensional finite element models place prohibitive demands on computational resources, and are not economically feasible. In this paper a similar layer-wise laminated shell theory is developed for doubly curved thick composite panels subjected to different combinations of three-dimensional boundary conditions. Piece-wise continuous, quadratic interpolation functions through the thickness, are combined with beam function expansions in the two in-plane directions of the laminate, to model the dynamic behavior of laminated spherical panels. This captures the discontinuities in the transverse shear and other strain distributions, from one layer to another. Past development of dynamic analyses of such structures using layer-wise theories were limited to flat plates. The present study is applicable to spherical laminates of arbitrary lamination sequence, and allows a generalized choice of boundary conditions which can be varied arbitrarily through the thickness. Preliminary results for spherical shells are presented and compared with existing results from other analytical methods in the literature. The ability of this layer-wise model to capture in-plane modes is illustrated. Particular attention is paid to the stiffening due to the spherical curvature, and to the influence of three-dimensional layer-wise boundary conditions on the natural frequencies and mode shapes.