Harnessing Auxetic Metamaterial Intelligence: Free Vibration of Graphene-Origami Curved Shells with Active Piezo-Composite Skins

Abstract

The present theoretical work explores the free vibration-based investigation of sandwich shell in the doubly-curved form with a core of functionally graded auxetic metamaterial graphene origami sandwiched by piezoelectric/piezomagnetic layers. The analytical framework is based on a simplified higher-order shear deformation theory. For a simply supported, functionally graded doubly-curved shell, the governing equations are established using Hamilton's principle. A Navier-type solution technique is then applied to obtain analytical results, which form the basis for a comprehensive parametric analysis. The frequencies are obtained in terms of material/geometric parameters such as weight fraction of graphene origami, folding degree, various pattern distributions, temperature, length-to-thickness ratio, and thicknesses of piezoelectric/piezomagnetic layers relative to the core shell thickness, considering various shell types. The numerical results indicate that the X-W_Gr pattern with higher h_p/h_e ratios are more beneficial for high-frequency applications, showing highest frequencies, specifically when applied to higher-curvature shells. Conversely, the V-W_Gr pattern, with its asymmetric distribution contribute more lower-curvature shells like the hyperbolic and flat plate shells.