On the viscoelastic carbon nanotube mass nanosensor using torsional forced vibration and Eringen’s nonlocal model

Abstract

This article aims to investigate the forced and free dynamic torsional vibrations of single-walled carbon nanotube (SWCNT) embedded in a viscoelastic medium under a harmonic external torque. Eringen’s nonlocal elasticity is established. It takes the effect of the small size into the formulation due to dealing with nanostructures. The governing equation and corresponding boundary condition are derived using Hamilton’s principle. The boundary condition is considered clamped-disk. In order to reduce the derived partial differential equation (PDE) to ordinary differential equation (ODE) one and discretizing, a Galerkin method is employed in the time domain. The novelty of the present work is that it seeks to investigate the dynamic angular displacement in a viscoelastic SWCNT subjected to an external torque and mass nanosensor over time for the first time. A harmonic load along with determined amplitude is applied to SWCNT. Subsequently, the effects of the nonlocal parameter, damping ratio, damping coefficient, stiffness of the viscoelastic medium, excitation frequency, geometry, and disk’s mass moment of inertia on the angular displacement, in the time domain, are demonstrated. For free torsional vibration, the undamped natural frequency based on the mass moment of inertia of the disk is calculated for the first three mode numbers. Afterward, the effects of the damping coefficient on the real and imaginary parts of the eigenfrequency are investigated. Also, the effects of the stiffness of the viscoelastic medium, nonlocal parameter, and the length on the real part of the eigenfrequency are reported. Furthermore, the effects of the nonlocal parameter and damping coefficient on the damping ratio are illustrated schematically. A finite difference method (FDM) is established to assess the exact solution. Moreover, the results are validated with another study. The results are compatible in comparison with each other.