Fully spatial nonlocal-mechanical analyses of magnetically affected layer-by-layer graphene structures as bi-directional electric currents’ transporters

Abstract

Over the past two decades, graphene sheets have been the focus of attention in interdisciplinary research activities as one of the most promising materials for effectively transporting electric currents due to their brilliant physical and chemical properties. However, up till now, almost no research has been devoted to the main nanomechanical aspects of magnetically affected multi-layer graphene sheets as bilateral electric current carriers. To fill this pivotal scientific gap within the context of the nonlocal differential/integral elasticity theory, a continuum-based Mindlin plate theory is methodically established to examine the mechanical characterizations of the current-carrying nanosystem in the presence of an in-plane bi-directional magnetic field (IBMF). For this purpose, the static and dynamic portions of the induced electromagnetic forces are originally derived on the basis of the Biot-Savart law and then effectively adopted in constructing the three-dimensional-integro-based equations of motion. Due to the serious challenges pertinent to extracting analytical or explicit solutions for such a specific class of three-dimensional integro-partial differential equations, the Galerkin mode-based approach is introduced as an effective tool to analyze them. The results obtained from this approach demonstrated a satisfactory agreement with the exact solutions and thereby encouraged us to a detailed discussion on the effects of key factors on the fundamental frequency and static deformation. The results reveal that while electric current can induce dynamic instability in nanosystems, applying the IBMF substantially increases the fundamental frequency and postpones this instability. These findings highlight IBMF’s potential to enhance the stability of graphene-based nanosystems, providing a solid foundation for designing reliable graphene-based nanosystems for advanced electrical applications.

Graphical abstract