Eur. Phys. J. Plus (2017) 132: 393
https://doi.org/10.1140/epjp/i2017-11688-0

Regular Article

Torsional vibration of nano-cone based on nonlocal strain gradient elasticity theory

¹ Department of Mechanical Engineering, Sousangerd Branch, Islamic Azad University, Sousangerd, Iran
² School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
³ Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
⁴ Engineering Graphics Center, Sharif University of Technology, Tehran, Iran

^* e-mail: amin.hadi@ut.ac.ir

Received: 30 May 2017
Accepted: 21 August 2017
Published online: 18 September 2017

Abstract

This paper investigates free torsional vibration behavior of a nonlinear nano-cone, based on the nonlocal strain gradient elasticity theory. The nano-cone is made of homogeneous and isotropic materials. Moreover, the cross-sectional area of the nano-cone varies in the longitudinal direction by a nonlinear function. Governing equation and boundary conditions are derived using Hamilton’s principle. These equations are solved by employing the generalized differential quadrature method (GDQM). The effects of some parameters, such as cross-sectional area change and small-scale parameter, are investigated. Results show that the cross-sectional area change has a significant effect on the torsional vibration behavior of the nano-cone. These results are also compared with the results reported in the literature, which shows consistency.