Study on size-dependent vibration and stability of DWCNTs subjected to moving nanoparticles and embedded on two-parameter foundations

Abstract

Parametric resonance is an important phenomenon that may be evinced in applying carbon nanotubes for the delivery of nanoparticles. This paper aims to investigate dynamics instability of double-walled carbon nanotubes (DWCNTs) surrounded by elastic medium and excited by a sequence of moving nanoparticles. The DWCNT is modeled as two Euler-Bernoulli beams interacting between them through van der Waals (vdW) forces. Based on Eringen's nonlocal elastic theory to consider the small-scale effects, the governing equations are derived by using Hamilton's principle. All inertial terms of the moving nanoparticles are taken into account. In addition, the van der Waals force between the constitutive atoms of the moving nanoparticle and those of the nanotube is considered. By utilization of the Galerkin method, the partial differential equations (PDEs) of motion are reduced to couple ordinary differential equations with time-varying coefficients describing a parametrically excited nanosystem. Then, an incremental harmonic balance (IHB) method is implemented to calculate the instability regions of the DWCNT. The results show that considering the vdW effects, increasing the amplitude of the static axial tensile force, reducing the amplitude of axial oscillating force, and increasing the stiffness of the elastic medium improve stability of the system. A comparison between the results with those reported in the literature is performed to verify the precision of the presented analyses.