Evaluation of various through the Thickness and Curvature approximations in Free vibration analysis of cylindrical Composites Shells

This paper presents a comparison of various, significant shell theories to evaluate the free vibration response of multi-layered, orthotropic cylindrical shells. Carrera unified formulation for the modelling of composite spherical shell structures is adopted. Via this approach, higher order, zig-zag, layer-wise and mixed theories can be easily formulated. As a particular case, the equations related to Love's approximations and Donnell's approximations and as well as of the corresponding classical lamination and shear deformation theories (CLT and FSDT) are derived. The governing differential equations of the dynamic problem are presented in a compact general form. These equations are solved via a Navier-type, closed form solution. Thin and moderately thick as well as shallow and deep shells are investigated. Several parametric analyses are carried out depending on the stacking sequences of laminates, on the degree of orthotropic ratio and the thickness and on the curvature parameters. Conclusions are drawn with respect to the accuracy of the theories for the considered lay-outs and geometrical parameters.