Statistical and parametric instability analysis for delivery of nanoparticles through embedded DWCNT

In this paper, the dynamic instability of double-walled carbon nanotubes (DWCNTs) enclosed by an elastic medium under parametric excitation of sequential moving nanoparticles has been analyzed. Using Hamilton’s principle, the governing equations are derived based on the Euler–Bernoulli beam theory. All inertial terms of the moving nanoparticles are taken into account and small-scale effects are applied in the dynamic formulation based on the Eringen’s nonlocal elastic theory. The incremental harmonic balance (IHB) technique is applied to estimate the parametric instability regions of the DWCNT carrying the moving nanoparticles. It is found that the stability of the system could be improved in some cases, such as taking into account the Van der Waals (vdW) effect, reducing the amplitude of axial oscillating force, enlarging the amplitude of the static axial tensile force and enhancing the stiffness of the elastic medium. The accuracy of the presented analyses is examined by comparing the results with those reported in the literature and very good agreement is observed. The results of this paper can be used in the design of advanced nano-electro-mechanical systems (NEMS) and nanodrug delivery systems, in which nanotubes act as the basic elements. •Dynamic instability of DWCNTs under excitation of moving nanoparticles is studied.•All inertial components of the nanoparticles are included in analyses.•The van der Waals effect of DWCNT layers is considered.•Numerical simulations are performed with Runge-Kutta method.