Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part II: Parametric studies

The possible usage of nanoplates in transporting of nanovehicles encouraged the author to propose some nonlocal plate models in the companion paper where the nanovehicle (i.e., moving nanoparticle) was modeled by a moving point load by considering its friction with the upper surface of the nanoplate. In this paper, a comprehensive parametric study is carried out to study the effects of length to thickness ratio of the nanoplate, small-scale parameter, and velocity (or angular velocity) of the moving nanoparticle on dynamic response of nonlocal Kirchhoff, Mindlin, and higher-order plates subjected to a moving nanoparticle. Herein, dynamic response of the nanoplate covers both time histories and dynamic amplitude factors of the in- and out-of-plane displacements. The capabilities of various nonlocal plate models in predicting the displacement field caused by friction and mass weight of the moving nanoparticle are then explored through various numerical analyses for two cases: (i) the moving nanoparticle moves along a diagonal of the nanoplate; (ii) the moving nanoparticle orbits on an ellipse path whose center is coincident with the nanoplate's center. The obtained results indicate that due to the incorporation of small-scale effect into shear strain energy of the nanoplate, an appropriate nonlocal plate model should be used. The results show that the choice of the nanoplate model to use relies on the small-scale parameter, geometrical properties of the nanoplate, and velocity of the moving nanoparticle.

A comprehensive parametric study is carried out to study the effects of length to thickness ratio of the nanoplate, small-scale parameter, and velocity (or angular velocity) of the moving nanoparticle on the dynamic response of nonlocal Kircchoff, Mindlin, and higher-order plates under a moving nanoparticle. The capabilities of various nonlocal plate models in predicting the displacements caused by friction and mass weight of the moving nanoparticle are also explored through various numerical analyses.In the presented figure, the normalized time history plots of w0 at location of the moving nanoparticle, when it orbits on an ellipse path, have been presented for different values of major length to minor length ratio and angular velocity of the moving nanoparticle: (a) b0/a0=1, (b) b0/a0=5, (c) b0/a0=10; ((∇)ωN=0.2, (◊)ωN=0.4, (△)ωN=0.6; (. . .) NKPT, (–.–) NMPT, (—) NHOPT; μ1=0.05; a/tp=15; ξ0=η0=0.5, a¯0=1/20).Figure optionsDownload as PowerPoint slideHighlights
► The role of influential factors on the dynamic responses of nanoplates is examined.
► The effects of various factors on DAFs of displacements of nanoplates are explored.
► The small-scale effect is also incorporated into the shear energy of the nanoplate.
► The capabilities of the proposed models are scrutinized through various examples.
► The selected model also relies on the small-scale effect and nanoparticle velocity.