Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading

This paper presents a simple solution of the dynamic stability of functionally graded shells under periodic axial loading based on large deflection theory. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The equations of motion are solved by Galerkin procedure. Bolotin’s method is then employed to obtain the steady-state vibrations for non-linear Mathieu equations. The effect of the volume fraction of the material constituents and their distribution on the parametric resonance, in particular steady-state vibrations amplitude and also the effect of the length-to-radius and thickness-to-radius ratios of the cylinder are examined and compared. A good agreement is obtained by comparing the present analysis with other available literature.