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Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity

  • Noroozi, Reza (School of Mechanical Engineering, College of Engineering, University of Tehran) ;
  • Barati, Abbas (Department of Mechanical Engineering, University of Guilan) ;
  • Kazemi, Amin (School of Mechanical Engineering, College of Engineering, University of Tehran) ;
  • Norouzi, Saeed (School of Mechanical Engineering, College of Engineering, University of Tehran) ;
  • Hadi, Amin (Cellular and Molecular Research Center, School of Medicine, Yasuj University of Medical Sciences)
  • Received : 2019.01.08
  • Accepted : 2019.12.17
  • Published : 2020.01.25
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Abstract

In this paper, for the first time based on the nonlocal strain gradient theory the effect of size dependency in torsional vibration of bi-direction functionally graded (FG) nonlinear nano-cone is study. The material properties were assumed to vary according to the arbitrary function in radial and axial directions. The Navier equation and boundary conditions of the size-dependent bidirectional FG nonlinear nano-cone were derived by Hamilton's principle. These equations were solved by employing the generalized differential quadrature method (GDQM). The presented model can turn into the classical model if the material length scale parameters are taken to be zero. The effects of some parameters, such as inhomogeneity constant, cross-sectional area parameter and small-scale parameters, were studied. As an essential result of this study can be stated that an FG nano-cone model based on the nonlocal elasticity theory behaves softer and based on the strain gradient theory behaves harder.

Keywords

References

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