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.

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

Dimitri, Rossana;Tornabene, Francesco
2019

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/430308
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