A LAYER-WISE ANALYSIS FOR FREE-VIBRATIONS OF THICK COMPOSITE SPHERICAL PANELS

The authors have previously presented layer-wise models for modeling t he vibrations of thick composite cylindrical shells. The layer-wise th eory is needed to overcome the deficiencies of conventional shear-defo rmable plate theories because the gradients of the deformation field a re not necessarily continuous through the thickness, due to the discon tinuity of material properties at layer interfaces. Fully three-dimens ional 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 thic k composite panels subjected to different combinations of three-dimens ional boundary conditions. Piece-wise continuous, quadratic interpolat ion functions through the thickness, are combined with beam function e xpansions in the two inplane directions of the laminate, to model the dynamic behavior of laminated spherical panels. This captures the disc ontinuities in the transverse shear and other strain distributions, fr om 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 lamina tion sequence, and allows a generalized choice of boundary conditions which can be varied arbitrarily through the thickness. Preliminary res ults for spherical shells are presented and compared with existing res ults from other analytical methods in the literature. The ability of t his layer-wise model to capture in-plane modes is illustrated. Particu lar attention is paid to the stiffening due to the spherical curvature , and to the influence of three-dimensional layer-wise boundary condit ions on the natural frequencies and mode shapes.