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Advances in Nano Research
  Volume 8, Number 1, January 2020 , pages 13-24
DOI: https://doi.org/10.12989/anr.2020.8.1.013
 


Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity
Reza Noroozi, Abbas Barati, Amin Kazemi, Saeed Norouzi and Amin Hadi

 
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.
 
Key Words
    torsional vibration; bi-directional FGMs; nano-cone; GDQM; nonlocal strain gradient elasticity
 
Address
(1) Reza Noroozi, Amin Kazemi, Saeed Norouzi:
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran;
(2) Abbas Barati:
Department of Mechanical Engineering, University of Guilan, Rasht, Iran;
(3) Amin Hadi:
Cellular and Molecular Research Center, School of Medicine, Yasuj University of Medical Sciences, Yasuj, Iran.
 

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