A new method for determination of natural frequency in bending vibration mode of single-walled carbon nanotubes

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

علیرضا فتاحی واجاری ¹ (گروه مهندسی مکانیک، دانشگاه آزاد اسلامی واحد شهریار، شهریار، ایران)

Received: 2017-02-22 Accepted : 2017-12-05 Published : 2021-02-01

Keywords: Natural frequency, Doublet mechanics, Scale parameter, bending vibration, single-walled carbon nanotubes,

Abstract :

This paper investigates the bending vibration of single-walled carbon nanotubes based on a new theory called doublet mechanics with a scale parameter. A sixth order partial differential equation that governs the bending vibration for such nanotubes is derived. Euler-Bernoulli beam model is used in this paper. Using doublet mechanics, the relation between natural frequency and scale parameter is derived in the bending vibration mode. It is proven that scale parameter plays significant role in the vibration behavior of such nanotubes in lateral direction. Such effect decreases the natural frequency compared to the predictions of the classical continuum mechanics models. However, with increasing the tube length, the scale effect on the natural frequency decreases. To validate this method, the results obtained herein are compared with the existing nonlocal and molecular dynamics results and good agreement is observed. It is the first time that DM is used to model the bending vibration of carbon nanotube.

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