A comparison of micro-mechanical modeling of asphalt materials using finite elements and doublet mechanics

Imam

2016

Z. Angew. Math. Phys.

This paper investigates the torsional vibration of single-walled carbon nanotubes (SWCNTs) using a new approach based on doublet mechanics (DM) incorporating explicitly scale parameter and chiral effects. A fourth-order partial differential equation that governs the torsional vibration of nanotubes is derived. Using DM, an explicit equation for the natural frequency in terms of geometrical and mechanical property of CNTs is obtained for both the Zigzag and Armchair nanotube for the torsional vibration mode. It is shown that chiral effects along with the scale parameter play a significant role in the vibration behavior of SWCNTs in torsional vibration mode. Such effects decrease the natural frequency obtained by DM compared to the classical continuum mechanics and nonlocal theory predictions. However, with increase in the length and/or the radius of the tube, the effect of the chiral and scale parameter on the natural frequency decreases.Mathematics Subject Classification. 70G60 · 70J30 · 35B99 · 00A72.

Section: Introductionmentioning

confidence: 99%

Torsional vibration of single-walled carbon nanotubes using doublet mechanics

Imam

2016

Z. Angew. Math. Phys.

“…Fatahi-Vajari and Imam studied vibration of SWCNTs using DM [32][33][34]. Some applications of doublet mechanics in biomechanics and nanomechanics are given in [35][36][37][38][39]. Owing to nanoscale dimensions of CNTs, it is difficult to set up controlled experiments to measure the properties of an individual CNT [40].…”

Section: Introductionmentioning

confidence: 99%

A new method for evaluating the natural frequency in radial breathing like mode vibration of double‐walled carbon nanotubes

2017

Z Angew Math Mech

This paper investigates the radial breathing like mode (RBLM) vibration of double-walled carbon nanotubes (DWCNTs) based on a new theory called doublet mechanics (DM) with a scale parameter. To this end, DWCNTs are considered as two concentric elastic thin cylindrical shells bounded together with van der Waals (vdW) forces between them. The vdW forces are modeled using Len-Jones potential. Using DM, two coupled second order partial differential equations that govern the RBLM vibration of DWCNTs are derived. Subsequently, the equations of motion are solved to obtain the natural frequencies in the RBLM vibration. It is the first time that DM is used to derive the natural frequencies of the RBLM vibration for DWCNTs. The advantage of these analytical formulas is that unlike the other methods, they are explicitly dependent to scale parameter and chirality effect. It is shown that the chirality and scale parameter play significant role in the RBLM vibration response of DWCNTs. To validate the accuracy and efficiency of this work, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed.

“…Fang et al [13] studied plane wave propagation in a cubic tetrahedral assembly using DM. Additional applications of doublet mechanics are given in [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Analysis of radial breathing mode of vibration of single‐walled carbon nanotubes via doublet mechanics

Imam

2016

Z Angew Math Mech

This paper investigates the radial breathing mode (RBM) vibration of single-walled carbon nanotubes (SWCNTs) based on doublet mechanics (DM) with a length scale parameter. A second order partial differential equation that governs the RBM vibration of SWCNTs is derived. Using DM, the relation between natural frequency and length scale parameter is derived in the RBM mode of vibration. It is shown that the length scale parameter plays significant role in the RBM vibration response of SWCNTs. The length scale parameter decreases the natural frequency of vibration compared to the predictions of the classical continuum models. However, with increase in tube radius, the effect of the scale parameter on the natural frequency decreases. The results obtained herein are compared with the existing theoretical and experimental results and good agreement with the latter is observed.