Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading

In this paper, a formulation for the dynamic stability analysis of functionally graded shells under harmonic axial loading is presented. A pro®le for the volume fraction is assumed and a normal-mode expansion of the equations of motion yields a system of Mathieu±Hill equations the stability of which is analyzed by the BolotinÕs method. The present study examines the e€ects of the volume fraction of the material constituents and their distribution on the parametric response, in particular the positions and sizes of the instability regions