Free vibration of a short-fiber-reinforced viscoelastic nanotube with non-local strain gradient theory

Abstract This study investigates the free vibration behavior of short-fiber-reinforced nanotubes incorporating viscoelastic material damping and small-scale effects. The system is modeled with rotational springs at both ends to represent deformable boundary conditions. The nonlocal strain gradient theory is employed to account for size-dependent behavior, while the Kelvin–Voigt model is used to introduce viscoelastic damping. The governing equations are derived via Hamilton’s principle. A semi-analytical solution based on Fourier sine series and Stokes' transformation is presented, leading to a general eigenvalue problem that includes reinforcement effects, rotational spring, non-local, strain gradient, and viscoelastic parameters. A key novelty of the proposed model is that classical boundary conditions (clamped or simply supported) are recovered simply by adjusting the rotational spring stiffness, without reformulating the problem. Numerical results illustrate the influences of various parameters such as fiber volume fraction, length-scale parameters, and viscous damping coefficient on the natural frequencies of the nanotube. It is shown that increasing the rotational spring stiffness raises the frequencies, whereas the viscoelastic damping reduces it and introduces complex frequency modes.