Dynamic stability of functionally graded piezoelectric circular cylindrical shells

A three-dimensional theoretical analysis of the dynamic instability region of functionally graded (FG) piezoelectric circular cylindrical shells is presented. The shells are subjected to a combined loading of periodic axial compression and electric field in the radial direction. A set of Mathieu-Hill equations governing the instability problem is derived and analyzed by Bolotin's method. Obtained results show that the unstable region of the structure is controlled by its geometric parameters, rigidity of material, and the imposed loading. The converse piezoelectric effect only slightly affects the unstable region. However, the direct piezoelectric effects play a significant role in changing unstable regions corresponding to the high order circumferential modes. It is also found that the dynamic stability regions for the considered FG piezoelectric shells are not sensitive to the inhomogeneity parameter.