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

Abstract

This paper presents an investigation on the dynamical properties of single-walled carbon nanotubes (SWCNTs), and 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, and 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 are investigated. A travelling wave moving along the circumferential direction of the SWCNT is observed.

Applicability and Limitations of Simplified Elastic Shell Theories for Vibration Modelling of Double-Walled Carbon Nanotubes

“…Refs. [57][58][59][60][61] demonstrated the excellent agreement of the natural frequencies of SWCNTs and MWCNTs obtained by considering Sanders-Koiter shell theory with the results of experimental studies and MD simulations, for a large range of geometries and wavenumbers. Therefore, in the present work, the Sanders-Koiter shell theory is assumed as the reference theory for the investigation of applicability and limitations of the simplified thin elastic shell models.…”

Applications of Graphene-Based Materials in Sensors: A Review

“…When carbon nanotubes are used in sensors and other fields, the vibration characteristics determine the working state and performance of the sensor [8]; The deformability and transmittance of carbon nanotube reinforced materials also depend on the vibration characteristics [8]. Therefore, studying the oscillation of carbon nanotubes is conducive to researchers to better understand the mechanical properties of carbon nanotubes and explore the application fields of carbon nanotubes [9]. The author believes that although carbon nano and graphene have similar predecessors, they may have different futures.…”

Chitosan-Based Flexible Memristors with Embedded Carbon Nanotubes for Neuromorphic Electronics

“…Therefore, CNTs are used in a variety of applications, including solar cells, supercapacitors, and electric double-layer capacitors (EDLCs) [ 21 , 22 ]. Furthermore, the high thermal conductivity of CNTs makes them suitable as a nanofiller to increase the thermal conductivity of polymeric materials, and extensive studies have been conducted regarding the high internal resonance and large energy exchange properties of polymer/CNT nanocomposite systems [ 23 , 24 , 25 , 26 ].…”