3D Size-Dependent Dynamic Instability Analysis of FG Cylindrical Microshells Subjected to Combinations of Periodic Axial Compression and External Pressure Using a Hermitian Finite Layer Method Based on the Consistent Couple Stress Theory.

This work develops a three-dimensional (3D) weak formulation, based on the consistent couple stress theory (CCST), for analyzing the size-dependent dynamic instability behavior of simply-supported, functionally graded (FG) cylindrical microshells that are subjected to combinations of periodic axial compression and external pressure. In our formulation, the microshells are artificially divided into layers. The displacement components of each individual layer are selected as the primary variables, which are expanded as a double Fourier series in the in-plane domain and are interpolated with Hermitian polynomials in the thickness direction. Incorporating the layer-wise displacement models into our weak formulation, we develop a Hermitian finite layer method (FLM) for addressing the current issue. The accuracy and the convergence rate of our Hermitian FLM are validated by comparing the solutions it produces with the accurate two-dimensional solutions of critical loads and critical pressures of FG cylindrical macroshells and single-walled carbon nanotubes, which were reported in the literature. The numerical results show the effects of the material length-scale parameter, the inhomogeneity index, the radius-to-thickness and length-to-radius ratios, the load magnitude ratio, and the static and dynamic load factors on the first principal and first secondary instability regions of parametric resonance of simply-supported FG cylindrical microshells are significant.