Large amplitude vibrations of anisotropic cylindrical shells

A semi-analytical method is developed in conjunction with shearable shell theory and modal expansion approach to predict the influence of geometrical non-linearities on free vibrations of anisotropic laminated cylindrical shells. Shear deformation and rotary inertia effects are taken into account in the equations of motion. The hybrid method developed in this theory is a combination of classical finite element approach, shearable shell theory and modal coefficient procedure. The displacement functions are obtained by the exact solution of the equilibrium equations of anisotropic cylindrical shells and thereafter, the mass and linear stiffness matrices are derived by exact analytical integration. Green exact strain–displacement relations are used to obtain the modal coefficients for these displacement functions. The second- and third-order non-linear stiffness matrices are then calculated by precise analytical integration and superimposed on the linear part of equations to establish the non-linear modal equations. The linear and non-linear natural frequency variations are determined as a function of shell parameters for different cases. The comparison shows that the numerical analysis is of good reliability on the prediction of the experimental results.