The effect of material and geometry on the non-linear vibrations of orthotropic circular cylindrical shells

• Non-linear dynamic analysis of an orthotropic cylindrical shell.
• Influence of the constitutive model on vibration frequencies and buckling loads.
• Influence of the material and geometrical parameters on the shell non-linearity.
• Bifurcation analysis of the shell in the main resonance region.
• Identification of coexisting solution for the shell under external forcing.

The extensive use of circular cylindrical shells in modern industrial applications has made their analysis an important research area in applied mechanics. In spite of a large number of papers on cylindrical shells, just a small number of these works is related to the analysis of orthotropic shells. However several modern and natural materials display orthotropic properties and also densely stiffened cylindrical shells can be treated as equivalent uniform orthotropic shells. In this work, the influence of both material properties and geometry on the non-linear vibrations and dynamic instability of an empty simply supported orthotropic circular cylindrical shell subjected to lateral time-dependent load is studied. Donnell׳s non-linear shallow shell theory is used to model the shell and a modal solution with six degrees of freedom is used to describe the lateral displacements of the shell. The Galerkin method is applied to derive the set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge–Kutta method. The obtained results show that the material properties and geometric relations have a significant influence on the instability loads and resonance curves of the orthotropic shell.