Combined influences of shear deformation, rotary inertia and heterogeneity on the frequencies of cross-ply laminated orthotropic cylindrical shells

The non-dimensional frequencies for symmetric and anti-symmetric cross-ply laminated heterogeneous composite circular cylindrical shells are analyzed by taking into account the effects of first-order deformations such as transverse shear deformations and rotary inertia. By using the Donnell-type shell theory, a set of fundamental dynamic equations of laminated circular cylindrical shells made of heterogeneous orthotropic materials is derived through Hamilton's principle. The basic equations are reduced to the six-order algebraic equation. One of the lowest positive roots of the algebraic equation represents the fundamental frequency. Attention is focused on the case of cross-ply laminated heterogeneous orthotropic cylindrical shells, from which solution for homogenous and heterogeneous orthotropic monolayer cylindrical shells follows based on classical shell theory (CST) and shear deformation theory (SDT), as a special case. Moreover, further detailed numerical results dealing with non-dimensional frequencies and corresponding mode shapes of laminated heterogeneous cylindrical shells having symmetric or anti-symmetric cross-ply lay-up are discussed. Furthermore, some comparisons are made to show the reliability and accuracy of the study.