Wave Dispersion in FG Graphene Origami Metamaterial Sandwich Cylindrical Microshells With Honeycomb Core Resting on Kerr Foundation and Conveying Fluid

This study explores the wave dispersion behavior of functionally graded (FG) graphene origami (Gori) metamaterial sandwich cylindrical microshells featuring a honeycomb core, resting on Kerr foundation, and conveying fluid. The study utilizes a sinusoidal four‐variable shear deformation shell theory, incorporating size effects via the modified couple stress theory. The core is characterized by a hexagonal honeycomb structure, whereas the upper and lower layers consist of FG graphene origami (Gori) metamaterial. The incompressible fluid‐microshell coupled system incorporates steady viscous forces from the fluid by utilizing time‐averaged Navier‐Stokes equations. Hamilton's principle is used to derive the system's partial differential equations, and an analytical solution is developed to examine the wave dispersion properties. The solution is validated through comparison with existing examples. The study explores how essential factors, such as foundation coefficients, material length scale, and shell geometry, influence the wave dispersion behavior. The analysis demonstrates that increasing the Gori weight fraction results in higher wave frequency and phase velocity, owing to the improved stiffness of the doubly‐curved shallow shell structure. Moreover, due to the increase in fluid pressure, which effectively enhances the dynamic stiffness of the shell, a rise in average flow velocity results in higher wave frequency and phase velocity.