A free vibration analysis of toroidal composite shells in free space

The main aim of this paper is to present a dynamic analysis of toroidal shell structures in free space. The simplified thin shell theory, based on the typical small deflection assumption, but enriched by the transverse shear terms, was used. The constituting material is not isotropic but a multilayer composite angle-ply laminate, with non-uniform thickness.A numerical procedure based on the classical Rayleigh–Ritz method, was utilized. The dynamic independent variables were expressed in terms of a double Fourier series expansion as function of the azimuth and internal meridian circular angle. This allowed to determine easily the strain and kinetic energy expressions, and consequently the stiffness and mass matrices.Then, the numerical problem was simplified to the classical generalized eigenvalue problem relation by differentiating the whole energetic functional, as in the Rayleigh–Ritz method. The solutions were determined by using an appropriate algorithm. The high frequency vibration modes were considered and their peculiarities with respect to the low frequency modes were pointed out. The dependence of the obtained results on the laminate winding angle was also considered.Comparisons with the other authors results were necessary to validate the utilized numerical approach.