Wave Dispersion Characteristics in a Doubly Curved Graphene Origami Shell Structure

This paper presents a comprehensive investigation into the wave propagation characteristics of a doubly curved shell structure fabricated from a novel composite material system. The core structure consists of copper (Cu), reinforced with a graphene origami auxetic metamaterial (GOAM). The shell is analyzed under the combined influence of uniformly distributed mechanical loads and transient/steady-state thermal loads, while being elastically supported by a Pasternak foundation (incorporating both shear layer and Winkler spring effects). To accurately characterize the effective thermo-elastic properties of this hierarchical nanocomposite (Cu/GOAM), micromechanical homogenization models are rigorously extended. These models explicitly account for the temperature-dependent properties of both the copper matrix and the graphene origami reinforcement, as well as critical microstructural parameters including: volume fraction, folding degree (governing the auxetic behavior of the origami structure), geometric characteristics (e.g. side length, thickness), and interfacial effects. The governing partial differential equations of motion, encompassing the effects of inertia, elastic deformation, thermal stresses, and foundation interaction, are derived based on shear deformation shell theory suitable for deep shells. The significant contribution of this work is investigating the effect of material and geometric parameters of the origami and double curved structure on the wave propagation responses of the shell. An analytical solution for the wave propagation is obtained employing Navier’s solution technique, applicable for shells with simply-supported edges on all edges. The accuracy and validity of the derived formulation, solution procedure, and computational implementation are systematically established through extensive comparative analyses with benchmark solutions and published results available in the open literature for analogous shell configurations and material systems.