An analytical study of the non-linear vibrations of functionally graded cylindrical shells subjected to thermal and axial loads

An analytical method and a new simplifying model of FG (functionally graded) cylindrical shells are presented based on Hamilton’s principle, Von Kármán non-linear theory and the first-order shear deformation theory, and subjected to thermal and axial loads. The coupled non-linear partial differential vibration equations are discretized based on a series expansion of linear modes and a multiterm Galerkin’s method. Neglecting the membrane inertias and rotary inertias, the equation of motion is transformed into a reduced equation in the generalised transverse displacement. Adopting multiple scales method, the amplitude frequency dependence and the non-linear forced frequency response are obtained in the case of a single mode assumption. The good agreement found was very satisfactory, in comparison with previous theoretical approaches. The purpose of this approach was to provide engineers and designers with an easy method for determining the non-linear vibration behaviour of FG cylindrical shells.