Prediction of small-scale effects on nonlinear dynamic behaviors of carbon nanotube-based nano-resonators using consistent couple stress theory

In this paper, the small-scale effects on the nonlinear dynamic mechanical and electromechanical behaviors of the carbon nanotubes and their applications as nano-resonators and electronic nano-filters are analyzed using the consistent couple stress theory. The dynamic formulations of the single-walled carbon nanotubes are developed using the Euler-Bernoulli beam model obtained by the consistent couple stress theory. The hypothesis considered for the applied theory is based on the recently developed technique to resolve the problem of indeterminacy in previous couple stress based-formulations. The results prove that this theory can be applied in analyzing the dynamic characteristics of the nanostructures in general and carbon nanotubes in particular and their possible applications in nano-electromechanical systems. According to the reported results, the developed formula can capture the small-scale effects increasing the stiffness, vibration frequency and dynamic pull-in voltages of the carbon nanotubes under electrostatic actuation.