A review of dynamic analyses of single- and multi-layered graphene sheets/nanoplates using various nonlocal continuum mechanics-based plate theories

This article is intended to present an overview of dynamic analyses of single-/multi-layered graphene sheets (SLGSs/MLGSs) and nanoplates with combinations of simply supported, free, and clamped edge conditions embedded in an elastic medium using various two-dimensional (2D) nonlocal continuum mechanics-based plate theories. Based on Hamilton’s principle incorporating Eringen’s nonlocal constitutive relations, the authors derive strong formulations of assorted 2D nonlocal continuum mechanics-based plate theories for the free vibration analysis of embedded SLGSs/MLGSs, including the nonlocal classical plate theory, the nonlocal first-order shear deformation plate theory (SDPT), the nonlocal refined higher-order SDPT, the nonlocal sinusoidal SDPT, the nonlocal exponential SDPT, and the nonlocal hyperbolic SDPT. Navier-type solutions based on these 2D nonlocal plate theories for free vibration problems of simply supported, SLGSs/MLGSs and nanoplates embedded in an elastic medium are obtained. Articles examining various mechanical behaviors of SLGSs/MLGSs and nanoplates using different nonlocal plate theories available in the literature are tabulated into categories, including bending, free vibration, buckling, dynamic instability, wave propagation, geometrically nonlinear bending, geometrically nonlinear vibration, and forced vibration analyses.