CHAOTIC RESPONSE ANALYSIS OF SINGLE-WALLED CARBON NANOTUBE DUE TO SURFACE DEVIATIONS

Nonlinear vibrational behavior of a single-walled carbon nanotube based mass sensors is considered. The modeling involves stretching of the mid plane and damping. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane due to the bridged boundary conditions. The manifestation of instability and chaos in the dynamic response is observed. The regions of periodic, sub-harmonic and chaotic behavior are clearly seen to be dependent on added mass and the surface deviations. Poincaré maps and frequency spectra are used to explicate and demonstrate the miscellany of the system behavior.

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The Dynamic Behaviour of Chiral, Fixed-Free, Single-Walled Carbon Nanotube-Based Nanomechanical Mass Sensors Due to Atomic Vacancies

Proceedings of the Institution of Mechanical Engineers Part N Journal of Nanoengineering and Nanosystems ◽

10.1243/17403499jnn179 ◽

2009 ◽

Vol 223 (2) ◽

pp. 45-56

Author(s):

A Y Joshi ◽

S P Harsha ◽

S C Sharma

Keyword(s):

Carbon Nanotube ◽

Dynamic Behaviour ◽

Single Walled Carbon Nanotube ◽

Single Walled Carbon ◽

Mass Sensors

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Nonlinear Dynamic Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

Journal of Nanotechnology in Engineering and Medicine ◽

10.1115/1.4005663 ◽

2011 ◽

Vol 2 (4) ◽

Cited By ~ 6

Author(s):

Anand Y. Joshi ◽

Satish C. Sharma ◽

S. P. Harsha

Keyword(s):

Carbon Nanotubes ◽

Carbon Nanotube ◽

Dynamic Response ◽

Beam Theory ◽

Central Plane ◽

Mass Sensor ◽

Poincaré Maps ◽

Single Walled Carbon Nanotube ◽

Poincare Maps ◽

Single Walled Carbon

In previous studies, experimentally measured resonance frequencies of carbon nanotubes have been used along with classical beam theory for straight beams. However, it is found that these carbon nanotubes are not straight, and that they have some significant surface deviation associated with them. This paper deals with the nonlinear vibration analysis of a wavy single-walled carbon nanotube based mass sensor, which is doubly clamped at a source and a drain. Nonlinear oscillations of a single-walled carbon nanotube excited harmonically near its primary resonance are considered. The carbon nanotube is excited by the addition of an excitation force. The modeling is carried out using the elastic continuum beam theory concept, which involves stretching of the central plane and phenomenological damping. This model takes into account the existence of waviness in carbon nanotubes. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass and the geometric imperfections of carbon nanotube. Poincaré maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

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Chaos of a Single-Walled Carbon Nanotube Resulting from Periodic Parameter Perturbation

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421501303 ◽

2021 ◽

Vol 31 (09) ◽

pp. 2150130

Author(s):

Zhen Wang ◽

Weipeng Hu

Keyword(s):

Carbon Nanotube ◽

Chaotic Behavior ◽

Parameter Perturbation ◽

External Excitation ◽

Subharmonic Solution ◽

Homoclinic Loop ◽

Single Walled Carbon Nanotube ◽

System Parameters ◽

Single Walled Carbon ◽

Excitation Parameters

Carbon nanotubes (CNTs) are used in various nano-electromechanical systems (NEMS), and the parameters (including the system parameters and the excitation parameters) may result in chaos in these systems. Thus, understanding the mechanism of the chaos arising from NEMS is vital for CNT’s applications. Motivated by this need, the chaotic properties of a single-walled carbon nanotube system resulting from parametric excitation and external excitation are investigated in this paper. The criteria for the existence of the chaotic behavior in the system with periodic and quasi-periodic perturbations are obtained by the homoclinic Melnikov and the second-order average methods. Furthermore, in order to show the connection between periodic motion and complex behavior, the subharmonic periodic solutions, inside and outside the homoclinic loop, are analyzed. The global structure and the saddle-node bifurcation of the unperturbed averaged system are also considered. Finally, the Poincaré section and the transversal intersection of the unstable and stable manifolds are presented to verify the occurrence of chaos or subharmonic solution. The simulation results confirm the correctness of the theoretical analysis.

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