Elasticity solution and free vibrations analysis of laminated anisotropic cylindrical shells

Dynamic response of axisymmetric arbitrary laminated composite cylindrical shell of finite length, using three-dimensional elasticity equations are st udied. The shell is simply supported at both ends. The highly coupled parti al differential equations are reduced to ordinary differential equations (O DE) with variable coefficients by means of trigonometric function expansion in axial direction. For cylindrical shell under dynamic load, the resultin g differential equations are solved by Galerkin finite element method, In t his solution, the continuity conditions between any two layer is satisfied. It is found that the difference between elasticity solution (ES) and highe r order shear deformation theory (HSD) become higher for a symmetric lamina tions than their unsymmetric counterpart. That is due to the effect of bend ing-streching coupling. It is also found that due to the discontinuity of i nplane stresses at the interface of the laminate, the slope of transverse n ormal and shear stresses aren't continuous across the interface. For free v ibration analysis, through dividing each layer into thin laminas, the varia ble coefficients in ODE become constants and the resulting equations can be solved exactly. It is shown that the natural frequency of symmetric angle- ply are generally higher than their antisymmetric counterpart. Also the res ults are in good agreement with similar results found in literatures.