Analytical Solutions of Thermal-Mechanical Vibration Models of Pinned-Pinned Fluid-Conveying Single-Walled Carbon Nanotubes Resting on Elastic Foundation

A. T. Adebusoye; A. A. Oyediran

A. T. Adebusoye Department of Mechanical Engineering University of Lagos, Lagos, Nigeria
A. A. Oyediran

Keywords: Euler-Bernoulli, nanotubes, Pasternak-type, Winkler elastic constant

Abstract

Pinned-pinned single-walled carbon nanotubes (SWCNTs) have attracted a lot of interest in recent years due to their suitability for a wide range of applications, such as field emission and vacuum microelectronic devices, nanosensors, and nanoactuators. Based on two simply supported beam-bending models and mode analysis, analytical solutions are developed in the present study to deal with the resonant frequency of a SWCNT. The resonant frequency shift of the pinned-pinned SWCNTs caused by change in temperature and interaction with both a Winkler and a Pasternak elastic medium are examined in order to explore the suitability of SWCNTs as a cooling device and resonators in quantum computer designs. The simulation results reveal that the increase in temperature and the non-local parameter decreases the resonant frequency. In contrast, the resonant frequency increases with increase in the stiffness of the elastic medium except that Tai-Ping Chang model is insensitive to changes in the Pasternak constant. Furthermore, the modified Haw-Long Lee model predicts a larger flutter compared to the modified Tai-Ping Chang et al. model. Therefore, the modified Tai-Ping Chang model is better used to analyze the thermal-mechanical vibration of a SWCNT.

References

Adebusoye, A.T., (2014). A comparative analysis of two models of thermal-mechanical vibration of pinned-pinned fluid-conveying single-walled carbon nanotubes resting on a two parameter elastic foundation, M.Sc. thesis, University of Lagos, Lagos, Nigeria.
Benzair, A., Tounsi, A., Heireche, H., Moulay, N., and Boumia, L., (2008). The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Appl. Phys, 41:10.
Blevins, R.D., (2001). Flow-induced vibration, Kreiger Publishing House, Kreiger drive, Malabar, Florida 32950, USA.
Chang, Tai-Ping, and Mei-Feng Liu, (2011). Thermal-Mechanical Vibration and Instability of a Fluid-Conveying Single-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory, In Proceedings of 2011 International Conference on Scientific Computing, 1(1): 55-58.
Dresselhaus, M. S., Dresselhaus, G., Charlier, J. C. and Hern�ndez, E., (2004). Electronic, thermal and mechanical properties of carbon nanotubes, Philosophical Transactions of the Royal Society of London, Sec A Maths Phys Eng Sci, 362:1823.
Eringen, A. Cemal, (1983). On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves�, J. Appl. Phys., 54: 4703�4710.