Nonlocal Continuum-based Modeling of a Nanoplate Subjected to a Moving Nanoparticle. Part I, Theoretical Formulations

The potential applications of nano plates in energy storage, chemical and biological sensors, solar cells, field emission, and transporting of nano cars have been attracted the attentions of the nanotechnology community to them during recent years. Herein, the later application of nano plates from non local elastodynamic point of view is of interest. To this end, dynamic response of a nano plate subjected to a moving nano particle is examined with in the context of non local continuum theory of Eringen. The fullysimply supported nanoplate is modeled based on the non local Kirchhoff, Mindlin, and higher-order plate theories. Thenon-dimensional equations of motion of the non local plate models are established. The effects of moving nano particle’s weight and existing friction between the surfaces of the moving nano particle and nano plate on the in-plane and out-of-plane vibrations of the nano plate are incorporated into the formulations of the proposed models. The eigen function expansion and the Laplace transform methods are employed for discretization of the governing equations in the spatial and the time domains, respectively. The analytical expressions of the dynamic deformation field associated with each non local plate theory are obtained when the moving nano particle traverses the nano plate on an arbitrary straight path (an opened path) as well as an ellipse path(a closed path). The dynamic in-plane forces and moments of each non local plate model are also derived. Furthermore, the critical velocity and the critical angular velocity of the moving nano particle for the proposed models are expressed analytically for the aforementioned paths. Part II of this work consists in a comprehensive
parametric study where the effects of influential parameters on dynamic response of the proposed
non local plate models are scrutinized in some detail.