Free Vibration Response of Shear-flexible Moderately-thick Orthotropic Cylindrical Shells

The free vibration response of shear-flexible moderately-thick orthotropic cylindrical shell panels, with fixed edges, is investigated using an analytical approach. The governing partial differential equations are developed based on Sander's kinematics and are solved using generalized Navier's with a boundary continuous double Fourier series expansion. The frequencies and mode shapes from the analytical solution for various parametric ratios, including degree of orthotropy (stiffness ratio), radius-to-segment ratio and segment-to-thickness ratio are compared with the finite element solutions that are based on an eight-node 48 degrees of freedom shell element. The rate of convergence of the analytical solution method with respect to the number of Fourier series terms, for various parametric ratios, is presented. The results of the analytical solution are very comparable to that of the finite element solution. It is clear that the presented analytical solution can be used as a benchmark to calibrate and validate numerical and finite element solutions that usually involve approximation to shell theories.