Size‐dependent vibration analysis of a FG viscoelastic nanotube attached with the time‐dependent boundary conditions using NLSGT

Abstract In this study, the torsional vibration of a functionally graded viscoelastic nanotube has been carried out under viscoelastic boundary conditions employing nonlocal strain gradient theory. First, the equation of motion of the problem has been established using Hamiltonian principles and the Kelvin–Voigt viscoelastic model. For the solution of the problem, the derivatives of the higher‐order Fourier series obtained with the help of Stokes' transforms have been utilized. Thus, an eigenvalue problem has been constructed from which the fundamental frequencies can be calculated. The results have been presented in tables and graphs, and it is observed that damping has a very important effect on torsional vibration. It has been also revealed that as the nonlocal length scale parameters and k (power‐law exponent) increase, the effect of damping decreases and as the strain gradient length scale parameter grows, the effect of damping rises.