Dynamic Instability of Vibrating Carbon Nanotubes Near Small Layers of Graphite Sheets Based on Nonlocal Continuum Elasticity
H. M. Sedighi, A. Yaghootian
Shahid Chamran University of Ahvaz, Ahvaz, Iran
Keywords: метод разложения по параметру, частотная кривая, углеродные нанотрубки, нелокальная теория упругости, силы притяжения Ван-дер-Ваальса, неустойчивость процесса притягивания, графитовые листы, parameter expansion method, frequency-amplitude relationship, carbon nanotubes, nonlocal elasticity theory, van der Waals attraction, pull-in instability, graphite sheets
Abstract
This article presents a new asymptotic method to predict dynamic pull-in instability of nonlocal clamped-clamped carbon nanotubes (CNTs) near graphite sheets. Nonlinear governing equations of carbon nanotubes actuated by an electric field are derived. With due allowance for the van der Waals effects, the pull-in instability and the natural frequency-amplitude relationship are investigated by a powerful analytical method, namely, the parameter expansion method. It is demonstrated that retaining two terms in series expansions is sufficient to produce an acceptable solution. The obtained results from numerical methods verify the strength of the analytical procedure. The qualitative analysis of system dynamics shows that the equilibrium points of the autonomous system include center points and unstable saddle points. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.
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