Nonlinear Dynamics of Electrically Actuated Carbon Nanotube Resonators

Abstract

This work presents an investigation of the nonlinear dynamics of carbon nanotubes (CNTs) when actuated by a dc load superimposed to an ac harmonic load. Cantilevered and clamped-clamped CNTs are studied. The carbon nanotube is described by an Euler–Bernoulli beam model that accounts for the geometric nonlinearity and the nonlinear electrostatic force. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the carbon nanotube. The free-vibration problem is solved using both the reduced-order model and by solving directly the coupled in-plane and out-of-plane boundary-value problems governing the motion of the nanotube. Comparison of the results generated by these two methods to published data of a more complicated molecular dynamics model shows good agreement. Dynamic analysis is conducted to explore the nonlinear oscillation of the carbon nanotube near its fundamental natural frequency (primary-resonance) and near one-half, twice, and three times its natural frequency (secondary-resonances). The nonlinear analysis is carried out using a shooting technique to capture periodic orbits combined with the Floquet theory to analyze their stability. The nonlinear resonance frequency of the CNTs is calculated as a function of the ac load. Subharmonic-resonances are found to be activated over a wide range of frequencies, which is a unique property of CNTs. The results show that these resonances can lead to complex nonlinear dynamics phenomena, such as hysteresis, dynamic pull-in, hardening and softening behaviors, and frequency bands with an inevitable escape from a potential well.

Theoretical investigation of nonlinear resonances in a carbon nanotube cantilever with a tip-mass under electrostatic excitation

“…However, except for tip mass effects, the nano-resonator had the PD bifurcation at subharmonic resonance branch only the under conditions of a high electrostatic field. 2,4 In this study, the tip mass effects led to the PD bifurcation of the system. These results show that the PD bifurcation occurred not only under high electrostatic forces but also with a tip mass effect, as illustrated in Fig.…”

“…Nano-devices that take advantage of the low density, high aspect ratio, and high conductivity of a CNT include nano-resonators [1][2][3][4] or mass sensors. [5][6][7] Nano-resonators are based on electromechanical resonance responses of a cantilevered CNT to electrostatic excitation.…”

Nonlocal modeling of a Carbon Nanotube actuated by an electrostatic force

“…On the other hand, the conventional continuum mechanics, adopted and assumed in many previous investigations [4,5], fails to predict the size dependence of such small-sized structures due to lacking of intrinsic length scales. Therefore, only recently, several higher-order elasticity theories have been presented to develop size-dependent continuum models.…”

Nonlinear Dynamic Analysis of Electrostatically Actuated Single-walled Carbon Nanotubes Using Nonlocal Elasticity

“…The first paper focused on the quality of charge distribution and the second one was about the stretching effects on the doubly clamped CNTs. In addition, Ouakad and Younis (2010) studied the dynamic behaviors of the CNTs under electrostatic actuation and presented the frequency response of the systems vs. different applied voltages. Rasekh and Khadem (2010) completed the researches conducted in the field of mathematical formulation of the CNT-based NEMS via more comprehensive results about static and dynamic behaviors of the CNTs under electrostatic and vdW forces.…”