Eur. Phys. J. Plus (2020) 135: 183
https://doi.org/10.1140/epjp/s13360-020-00207-z

Regular Article

Torsional dynamic response of viscoelastic SWCNT subjected to linear and harmonic torques with general boundary conditions via Eringen’s nonlocal differential model

¹ Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran
² Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran
³ Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Sidi Bel Abbès, Algeria

^* e-mail: hosseini@bzte.ac.ir

Received: 31 July 2019
Accepted: 12 January 2020
Published online: 1 February 2020

Abstract

The present work investigates the dynamic torsional vibrations in a single-walled carbon nanotube embedded in a viscoelastic medium under the linear and harmonic external torques. In order to derive the equation of motion and associated clamped–clamped and clamped–torsional spring boundary conditions, Hamilton’s principle is utilized. Eringen’s nonlocal elasticity theory is the selected theory to show the small-scale effect. The assumed modes method and a Galerkin method are applied to analyze the derived equation analytically as the exact solutions. Then, the Rayleigh–Ritz method is proposed to compare the obtained results. In free vibration analysis, the nonlocal parameter has an effect on both natural frequencies and energy dissipation in different modes. It should be emphasized that the forced analysis of torsional vibration in the viscoelastic nanoscale is novel. The variation of the nonlocal parameter, thickness of carbon nanotube, damping coefficient, stiffness of the boundary spring, as well as the influence of excitation frequency on the angular displacement in the time domain, are illustrated in this paper. The results desirably are consistent with those from other studies.