Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics

Abstract

In this paper, the small scaling parameter e0 of the nonlocal Timoshenko beam theory is calibrated for the free vibration problem of single-walled carbon nanotubes (SWCNTs). The calibration exercise is performed by using vibration frequencies generated from molecular dynamics simulations at room temperature. It was found that the calibrated values of e0 are rather different from published values of e0. Instead of a constant value, the calibrated e0 values vary with respect to length-to-diameter ratios, mode shapes, and boundary conditions of the SWCNTs. In addition, the physical meaning of the scaling parameter is explored. The results show that scaling parameter assists in converting the kinetic energy to the strain energy, thus enabling the kinetic energy to be equal to the strain energy. The calibrated e0 presented herein should be useful for researchers who are using the nonlocal beam theories for analysis of micro and nano beams/rods/tubes.

One-dimensional nonlocal elasticity for tensile single-walled carbon nanotubes: A molecular structural mechanics characterization

“…Duan et al [19] and Hu et al [20] calibrated the small-scale parameters for the free vibration problem in SWCNTs by using molecular dynamics simulations. They found that the estimated nonlocal parameters vary with the aspect ratio, mode shapes and boundary conditions of the SWCNTs.…”

Estimação do parâmetro não-local de um nanotubo de carbono de parede única via Inferência Bayesiana.

“…Com o uso de modelos não-locais de vigas, frequências naturais em nanotubos de carbono de paredeúnica e dupla foram determinadas e reportadas como coerentesàquelas conseguidas experimentalmente ou por métodos baseados em dinâmica molecular [7]. Contudo, o fator não-local deve ser estimado, Duan et al [2] efetuaram a calibração do fator de escala a partir de resultados de frequências naturais por dinâmica molecular.…”

Vibrational Behavior of Single-Walled Carbon Nanotubes Based on Donnell Shell Theory Using Wave Propagation Approach

“…It can be observed from Tables 1 and 2 that the length-to-diameter ratio of the set of C-C SWCNTs is somewhat dissimilar from that of C-F SWCNTs. For the prediction of mechanical characters [7,[19][20][21] from atomistic studies and the experimental studies [5,6,[33][34][35][36][37][38] are often used for the clamped-free carbon nanotubes. The frequencies for the first and third modes obtained from present model which is compared with molecular dynamic simulation and Timoshenko beam model are shown in Figure 3.…”