Dynamic stability analysis of functionally graded three-dimensional graphene foam cylindrical microshells under interior pressure based on modified strain gradient theory

In this study, the dynamic stability of microshells made of functionally graded (FG) three-dimensional graphene foams (3D-GrFs) is examined through the utilization of the first-order shear deformation theory and the modified strain gradient theory. The material properties of FG 3D-GrFs microshells gradually change along the thickness direction as the gradient distribution of internal foams. Two different patterns of foam distribution in microshells thickness direction, namely as 3D-GrFs-1 and 3D-GrFs-2, are considered. The Rayleigh-Ritz method, in conjunction with energy functions, is applied to construct the governing equations of FG 3D-GrFs microshells under different boundary conditions. Moreover, the governing equations are transformed to Mathieu-Hill equations and then the unstable regions are presented with the aid of Bolotin's method. Detailed parametric studies are performed to highlight the effects of end supports, geometrical parameters, foam coefficient, foam distribution, interior pressure, dimensionless length scale parameter and circumferential wave number on the dynamic stability characteristics of FG 3D-GrFs microshells.