Vibration of nonlocal Kelvin–Voigt viscoelastic damped Timoshenko beams

This paper investigates the dynamic behavior of nonlocal viscoelastic damped nanobeams. The Kelvin–Voigt viscoelastic model, velocity-dependent external damping and Timoshenko beam theory are employed to establish the governing equations and boundary conditions for the bending vibration of nanotubes. Using transfer function methods (TFM), the natural frequencies and frequency response functions (FRF) are computed for beams with different boundary conditions. Unlike local structures, taking into account rotary inertia and shear deformation, the nonlocal beam has maximum frequencies, called the escape frequencies or asymptotic frequencies, which are obtained for undamped and damped nonlocal Timoshenko beams. Damped nonlocal beams are also shown to possess an asymptotic critical damping factor. Taking a carbon nanotube as a numerical example, the effects of the nonlocal parameter, viscoelastic material constants, the external damping ratio, and the beam length-to-diameter ratio on the natural frequencies and the FRF are investigated. The results demonstrate the efficiency of the proposed modeling and analysis methods for the free vibration and frequency response analysis of nonlocal viscoelastic damped Timoshenko beams.