Dynamic analysis of magnetically sensitive embedded graphene nanoplate using nonlocal elasticity and smooth GFEM approximation

Graphene has gained great relevance in the engineering community in the development of nanotechnologies. Studying the mechanical behavior of graphene nanoplates subjected to a magnetic field has become an important concern in the development of nanodevices, such as nanocomposites, nanosensors, and nanoelectromechanical systems. Given this scenario, this work aims at investigating the dynamic behavior of graphene nanoplates embedded in an elastic medium - which can be the case in graphene-reinforced nanocomposites - and subjected to a in-plane unidirectional magnetic field. The interaction of the graphene nanoplate with the surrounding elastic medium is represented by means of a Winkler elastic foundation. The influence of the in-plane unidirectional magnetic field is represented by the Lorentz force. The bending deformation is modeled using a first-order shear deformation theory, and the material is assumed to follow an isotropic nonlocal elasticity theory. The generalized finite element method (GFEM) is used for the numerical analysis. The approximation spaces are built from the homogeneous ?????? version of GFEM using partition of units (PUs) with regularity C ??????, ?????? = 2, 4. The study takes into account various dynamic conditions, including forced, unforced, and free vibrations. The influence of the approximation space smoothness on the first fundamental frequency is evaluated for free and unforced problems. The analysis involves a parametric assessment of the nanoplates' sizes, the magnetic field's strength, and the nanoscale coefficient. The influence of the approximation smoothness is also examined for the case of forced vibrations by analyzing the vertical displacement at the plate center as well as both softening and resonance phenomena. The results obtained using the proposed numerical framework are compared with those from (i) molecular dynamics (MD); (ii) Hermite C1 finite elements; (iii) Lagrangian C0 finite element; and (iv) semi-analytical solutions (which are used as reference solution). This study found that high regularity models correctly predicted the nanoplate dynamic behavior accounting for the effective structural stiffness due to nonlocal effects and the presence of a magnetic field. In this sense, high regularity approximation spaces yielded findings that were substantially more accurate than high order FEM C0 simulations.