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The possibility of moving drug materials into the intelligent nano-materials such as nanotubes such as set of DNA or RNA molecules to change the behavior of cells is an important problem in the nano-medicine science. This paper deals with vibrational control of magnetically thermally affected single-walled carbon nanotube (SWCNT) under a moving nanoparticle using the nonlocal-strain gradient theory based on the Rayleigh beam model. The elastic medium is modeled as Pasternak substrate. A gain matrix with time-varying behaviors and displacement-velocity feedback in the framework of linear classical optimal control procedure is used to suppress the vibration responses of the SWCNT. Hamilton, Galerkin and Newmark time integration principles are jointly utilized to ascertain the equations of motion. The influences of the nonlocal and material length-scale parameters, the velocity of nanoparticle and physical fields on the vibration behavior of the SWCNT are explored. Likewise, a specified control algorithm in suppressing the vibrational behavior of SWCNT under the effect of moving nanoparticle is examined.

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Nowadays, the mechanical characteristics of micro-/nano-structures in the various types of engineering disciplines are considered as remarkable criteria which may restrict the performance of small-scale structures in the reality for a certain application. This paper deals with a comprehensive review pertinent to using the nonlocal strain-gradient continuum mechanics model of size-dependent micro-/nano-beams/-plates. According to the non-classical features of materials, using size-dependent continuum mechanics theories is mandatory to investigate accurately the mechanical characteristics of the micro-/nano-structures. Recently, the number of researches related to the analysis of micro-/nano-structures with various geometry including beams as well as plates is considerable. In this regard, the mechanical behavior of these structures induced by different loadings such as vibration, wave propagation, and buckling behavior associated with the nonlocal strain-gradient continuum mechanics model is presented in this review work. Proposing the most valuable literature pertinent to the nonlocal strain-gradient continuum mechanics theory of micro-/nano-beams/plates is the main objective of this detailed survey.