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Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory

  • Belmahi, Samir (Department of Civil Engineering, University of Ibn Khaldoun) ;
  • Zidour, Mohammed (Department of Civil Engineering, University of Ibn Khaldoun) ;
  • Meradjah, Mustapha (Laboratory of Materials and Hydrology, University of Djillali Liabes)
  • Received : 2018.05.07
  • Accepted : 2018.08.06
  • Published : 2019.01.25
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Abstract

This present article represents the study of the forced vibration of nanobeam of a single-walled carbon nanotube (SWCNTs) surrounded by a polymer matrix. The modeling was done according to the Euler-Bernoulli beam model and with the application of the non-local continuum or elasticity theory. Particulars cases of the local elasticity theory have also been studied for comparison. This model takes into account the different effects of the interaction of the Winkler's type elastic medium with the nanobeam of carbon nanotubes. Then, a study of the influence of the amplitude distribution and the frequency was made by variation of some parameters such as (scale effect ($e_0{^a}$), the dimensional ratio or aspect ratio (L/d), also, bound to the mode number (N) and the effect of the stiffness of elastic medium ($K_w$). The results obtained indicate the dependence of the variation of the amplitude and the frequency with the different parameters of the model, besides they prove the local effect of the stresses.

Keywords

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