Dynamic response of slacked single-walled carbon nanotube resonators

Abstract

This paper presents an investigation of the dynamics of electrically actuated single-walled carbon nanotube (CNT) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear shallow arch model is utilized. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNTs of higher and lower aspect ratio. Results of the perturbation method are verified with those obtained by numerically integrating the equations of a multi-mode reduced-order model based on the Galerkin procedure. The effective nonlinearity of the CNT is calculated as a function of the slack level and the DC load. To handle computational problems associated with CNTs of small radiuses, results based on a nonlinear cable model are also demonstrated. The results have indicated that the quadratic nonlinearity due to slack has dominant effect on the dynamic behavior of the CNT.

Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

“…As a case study, a non-hollow CNT of L = 1000 nm, Numerical response with the same parameter calculated without the Taylor expansion from previous study of [27] are plotted in the same figure with numerical results using the simplified governing equation with the electrostatic force term substituted as its Taylor series. It has been mentioned in [27] that to get this result is quite computationally challenging and time consuming due to the spatial integration involving the complex electrostatic force term at each time step.…”

“…It is worth to point out that one advantage of the Taylaor series expansion of the electrostatic force that it resolves the numerical problems reported in [27] when using a beam model, in which case a cable model had to be used. Here we do not face such a problem, and hence, we are able to keep the bending effect and use a beam model.…”

“…To derive a reduced-order model ROM, we apply the Galerkin method and use the undamped unforced beam's linear orthonormal modeshapes () i x  [25][26][27]. Hence the deflection is expressed as:…”

On-Chip Platform for Slack-Free Carbon Nanotube Resonators

“…In CNT resonant sensors, both as-grown and dry transferred CNTs over a trench usually have a slack [3] which alters the dynamic behavior of CNT resonators [4]. A nanotube with slack, shows both in-plane and out-ofplane resonances [5] below the fundamental flexural mode.…”

Coupling between flexural modes in free vibration of single-walled carbon nanotubes

“…24,25 The effect of initial curvature of CNTs has also been investigated using a two dimensional nonlinear curved beam model, and it shows the transfer of energy among the vibration modes involved in the veering phenomenon. 26,27 High temperatures lead to large-amplitude thermal vibration, along with geometric nonlinearity, which will have a significant effect on the thermal vibration behaviors of CNTs. Very recently, the thermally induced free nonlinear vibration of single-walled CNTs (SWCNTs) was investigated, the whirling motion of SWCNT tip which leads to multiple peaks of experimentally observed frequency spectra was found.…”