Linear vibrations of triple-walled carbon nanotubes

Abstract

This paper presents an investigation on the dynamical properties of single-walled carbon nanotubes (SWCNTs), nonlinear modal interaction and energy exchange are analysed in detail. Resonance interactions between two conjugate circumferential flexural modes (CFMs) are investigated. The nanotubes are analysed through a continuous shell model, a thin shell theory is used to model the dynamics of the system; free-free boundary conditions are considered. The Rayleigh-Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. The model is validated in linear field (natural frequencies) by means of comparisons with literature. A convergence analysis is carried out in order to obtain the smallest modal expansion able to simulate the nonlinear regimes. The time evolution of the nonlinear energy distribution over the SWCNT surface is studied. The nonlinear dynamics of the system is analysed by means of phase portraits. The resonance interaction and energy transfer between the conjugate CFMs is investigated. A travelling wave moving along the circumferential direction of the SWCNT is observed.

Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single‐Walled Carbon Nanotubes

“…To the authors' best knowledge, the present paper is the first work in which the travelling wave response in SWCNT, considered as "graphene sheet rolled into a seamless tube" [1], is observed in nonlinear field. Other relevant linear and nonlinear dynamic phenomena of CNTs can be found in [60][61][62].…”

Vibration analysis and pull-in instability behavior in multi walled piezoelectric nano-sensor with fluid flow conveyance: influences of surface/interface energy

“…And using dimensionless strain and kinetic energies Eqs. (5) and (6) and dimensionless applied works…”

“…Many studies have been carried out on the vibration and stability analysis of nanostructure that some of them are reviewed here. Strozzi and Pellicano investigated vibration analysis of triplewalled carbon nanotubes (TWNTs) subjected to the interlayer van der Waals (vdW) force in the framework of the Sanders-Koiter shell theory [5]. Also, based on nonlocal cylindrical shell theory, Ghorbanpour Arani et al studied nonlinear vibration and instability of the double walled boron nitride nanotubes [6].…”

Relationship between Viscosity, Microstructure and Electrical Conductivity in Copolyamide Hot Melt Adhesives Containing Carbon Nanotubes

“…The amount of these nanofillers required for electrically conductive network formation, identified by percolation threshold, is much lower in comparison to the metallic particles, usually between 1 and 3 wt % [ 14 ]. Compared to other types of carbon nanofillers, MWCNTs are characterized by excellent electrical properties (8 × 10 −6 ÷ 20 × 10 −6 Ωm), thermal conductivity (λ = 6600 W/mK at 100 K), a high Young’s modulus (1.7–2.4 TPa) and tensile strength (100 GPa) as well as low cost (100 EUR/1 kg) [ 15 , 16 ].…”