Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

Farokhi, Hamed, Païdoussis, Michael and Misra, Arun (2018) Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model. Journal of Sound and Vibration, 419. pp. 604-629. ISSN 0022-460X

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Abstract

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

Item Type:	Article
Uncontrolled Keywords:	Carbon nanotube resonator, Cantilevered nanosensor, Electrostatic load distribution, Nonlinear behaviour, Nonlinear damping, Modified couple stress theory, Finite element analysis
Subjects:	H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User:	Becky Skoyles
Date Deposited:	07 Aug 2018 10:33
Last Modified:	11 Oct 2019 19:01
URI:	http://nrl.northumbria.ac.uk/id/eprint/35207

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