Elastic waves in graphene origami-enabled auxetic metamaterial thickness-deformable doubly-curved shells

Abstract

This study, for the first time, investigates the bulk waves in mechanical metamaterial thickness- and shear-deformable doubly-curved shells; it considers spherical, elliptical, hyperbolic, and cylindrical shell structures. A third-order shear deformable model, involving thickness deformation, is employed to capture in-surface and out-of-surface, rotational, and stretching motions within a curvilinear coordinate system. Equations of motion are obtained via Hamilton’s principle, resulting in a set of coupled partial differential equations. A genetic programming-based micromechanics method for mechanical properties has been developed in the literature recently; this paper uses it as simulation inputs. A harmonic approach is used to solve these equations and to obtain the circular frequency. For the spherical, elliptical, hyperbolic, and cylindrical shells, influences of the curvatures on the wave frequency are highlighted. In the Appendix, a comparative analysis for a simplified case (excluding metamaterial effects, and multilayer configurations) demonstrates very good agreement with prior studies.