Abstract
It is aimed to investigate vibrations of an embedded nanoplate subjected to biaxially applied loads and a moving nanoparticle. To this end, the nanoplate and the moving nanoparticle in order are modeled via nonlocal Kirchhoff plate theory and a rigid body. The mass weight of the moving nanoparticle, and its friction with the upper surface of the nanoplate are taken into account in the proposed model. For a more general study of the problem, the dimensionless equations of motion are obtained. The in- and out-of-plane displacements of the nanoplate are discretized in the space and time using assumed mode and generalized Newmark-β methods, respectively. The roles of the moving nanoparticle velocity, small-scale parameter, biaxially tension forces, and the lateral stiffness of the surrounding medium on the displacements of the nanoplate are addressed and discussed.
Highlights
A nanoplate is commonly defined as a nanostructure whose thickness is fairly negligible in compare to other two dimensions
When a nanocar travels on the upper surface of a nanoplate, in- and out-of-plane waves would propagate within the nanoplate
The nanoplate is modeled according to Kirchhoff plate theory, and the moving nanoparticle is considered as a rigid body
Summary
A nanoplate is commonly defined as a nanostructure whose thickness is fairly negligible in compare to other two dimensions. In-plane and out-of-plane vibrations of a biaxially-tensioned embedded nanoplate due to movement of a nanoparticle on its upper surface are investigated via this advanced theory For this purpose, the nanoplate is modeled according to Kirchhoff plate theory, and the moving nanoparticle is considered as a rigid body. The nanoplate is modeled according to Kirchhoff plate theory, and the moving nanoparticle is considered as a rigid body Such a nanoparticle exerts its mass-weight and frictional forces on the upper surface of the embedded nanoplate. Outer surface of the nanoparticle and the upper surface of the nanoplate, denoted by μk mg where μk is the kinetic friction coefficient, is corresponding to the in-plane vibrations Such moving weight and friction forces should be appropriately taken into account in the proposed model.
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