Nonlocal anisotropic elastic shell model for vibrations of double-walled carbon nanotubes under nonlinear van der Waals interaction forces

In this paper, a novel nonlocal anisotropic elastic shell model is developed to investigate the nonlinear vibrations of double-walled carbon nanotubes (DWCNTs) in framework Sanders–Koiter theory. Van der Waals interaction forces between two concentric single-walled (SWCNTs) composing DWCNT are modelled via Lennard-Jones potential and He’s formulation. linear vibration analysis, displacement field each SWCNT expanded by means double mixed series terms Chebyshev orthogonal polynomials along longitudinal direction harmonic functions circumferential direction, Rayleigh–Ritz method considered get approximate natural frequencies modal shapes. three displacements re-expanded eigenfunctions derived an energy approach based on Lagrange equations adopted obtain set ordinary differential motion, which then solved numerically. Molecular dynamics simulations performed order calibrate proper value parameter be inserted constitutive proposed continuum model. A simplified distribution van initially analyse DWCNTs, obtaining hardening behaviour. By considering more realistic forces, stronger behaviour found. • for developed. adopted. The estimate from globally accurate than that local one. considered. response significantly given corresponding distribution.