Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part I: Theoretical formulations

► Using nonlocal continuum theory, a nanoplate under a moving nanoparticle is studied. ► The nanoplate is modeled using Kirchhoff, Mindlin, and higher-order plate models. ► The mass weight of the moving nanoparticle and the frictional force are considered. ► Using Laplace method, dynamic deformations of the proposed models are obtained. ► The critical velocity of the moving nanoparticle is derived for each nonlocal model.