Transient response of oscillated carbon nanotubes with an internal and external damping

The present works aims at modeling a viscoelastic nanobeam with simple boundary conditions at the two ends with the introduction of the Kelvin-Voigt viscoelasticity in a nonlocal strain gradient theory. The nanobeam lies on the visco-Pasternak matrix in which three characteristic parameters have a prominent role. A refined Timoshenko beam theory is here applied, which is only based on one unknown variable, in accordance with the Euler-Bernoulli theory, whereas the Hamilton's principle is applied to derive the equations of motion. These are, in turn, solved for a carbon nanotube with some fixed material properties. An analytical method has been used to discretize the equations in the displacement field and time, while computing the time-response of the system. For validation purposes, the results based on the proposed formulation are successfully compared to several references. A final parametric investigation focuses on the sensitivity of the time-response of a nanotube under simple boundary conditions, to different parameters such as the length scale, the viscoelasticity coefficients or the nonlocal parameter.