Non-linear free vibration analysis of laminated cylindrical shells under static axial loading including accurate satisfaction of boundary conditions

• The paper illustrates several key aspects related to the problem of non-linear vibrations of loaded shells.
• In the analysis the specified boundary conditions at the shell edges can be satisfied rigorously.
• Both the static and dynamic non-linear stress and deformation state can be accurately described.

The effect of a static preload on the non-linear vibration behaviour of laminated anisotropic shells is studied. Starting point of the analysis is a perturbation approach developed earlier to analyse the non-linear vibration behaviour of imperfect general structures under static preloading. This method is based on a perturbation expansion for both the frequency parameter and the dependent variables, and can be used to study the effects of geometric imperfections, a static fundamental state, and a non-trivial static state on the linearised and non-linear vibrations of cylindrical shells. The theory has been incorporated within a semi-analytical framework, based on Donnell-type governing equations.The approach is applied in the non-linear vibration analysis of laminated, anisotropic cylindrical shells. Special characteristics of the non-linear free vibration behaviour of statically, axially loaded cylindrical shells are shown for a specific composite shell. Internal resonances corresponding to interactions between first order modes and second order modes are found in the analysis. Novel aspect of the current work is that these phenomena are considered within a framework in which effects of various types of boundary conditions, including the effect of non-linear static state deformation due to the application of the static load, are accurately taken into account.