Torsional vibration analysis of viscoelastic functionally graded nanotubes with viscoelastic boundaries using lam’s strain gradient theory

Abstract In this study, the torsional vibration of viscoelastic FG nanotubes with viscoelastic boundary conditions has been investigated by considering the size effect. The size effect has been based on the strain gradient elasticity theory developed by Lam. The Kelvin-Voigt viscoelastic model has been employed to model the time-dependent material behavior. In order to solve the problem, an approach has been developed by combining the Fourier Sine series and the Stokes transform. At the end of this process, an eigenvalue problem has been achieved that determines the torsional vibration frequencies of the viscoelastic nanotube under Kelvin-Voigt viscoelastic boundary conditions. The eigenvalue problem provides a general solution including the length scale parameters of the material, the viscous damping coefficient and the viscoelastic boundary conditions. Thus, a highly flexible and efficient solution methodology has been proposed for examining the torsional vibration behavior of viscoelastic nanotubes under viscoelastic boundary conditions. Therefore, the present study is anticipated to provide a substantial contribution to the existing body of literature. The findings obtained from the study are presented in figures and tables; it has been observed that scale parameters and power-law exponent increase the damping effect, and in cases where viscous properties become dominant, the frequencies of higher modes can reach lower values than the first mode.