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Introduction <p>The aim of this study is driving and solving equations for the nonlinear damped transverse-torsional coupled vibrations of the single-wallcarbon nanotubes (SWCNTs) embedded in a viscoelastic medium (layer) in a three-dimensional magnetic-thermal environment.</p> Objective <p>The most importantobjective of this study is to investigate the presence of possibility of coupling between transverse and torsional vibrations for circular symmetric cross sectionSWCNT.</p> Method <p>The equations are derived such that the circular cross-sectional area of the SWCNTs does not results in decoupling the transverse andtorsional motions. The nonlocal theory is used to take into account the small size effect of the SWCNTs. The deformations are described by bending slope angleand twisting angle using Euler angles. Considering the higher nonlinear terms causes the coupling the transverse and torsional motions.</p> Conclusions <p>Theresults show that a torsional initial motion causes not only a torsional motion but also a transverse motion. At the high (elevated) temperatures, the transverseoscillations decrease in a coupled mode. Transverse and torsional frequencies affect each other in a coupled mode. The amplitude of the transverse oscillationsdepends on the values of various parameters including the temperature, value of damping constants, and boundary conditions, etc. The SWCNTs aresurrounded by a layer (viscoelastic medium) having transverse and torsional elastic and damping behaviors. The torsional frequencies remain constant for anyvalues of the stiffness of layer in the transverse direction. But torsional frequencies increase by increasing the torsional stiffness of the viscoelastic layer,because it applies a twisting moment to the nanotube. But the transverse frequencies will not change by changing the torsional stiffness of viscoelasticmedium. As the torsional damping constant of viscoelastic layer increases, the oscillations in the transverse and torsional directions decrease faster andbecome damped. For different values of the damping constants in the torsional direction, the amplitude of the torsional oscillations is the same at thebeginning and then with the passage of time, a higher value of the damping constant compared to a lower damping constant, causes a more reduction of theoscillation amplitude in the torsional direction.</p>

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Transverse-Torsional Couple Vibrations of Carbon Nanotubes Embedded in a Viscoelastic-Magnetic-Thermal Environment

  • 期刊论文

  • 发表日期：

    2025年6月16日

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  • Sardar S. Abdullah,
  • Shahrokh H. Hashemi,
  • Nazhad A. Hussein,
  • Reza Nazemnezhad

摘要

Introduction

The aim of this study is driving and solving equations for the nonlinear damped transverse-torsional coupled vibrations of the single-wallcarbon nanotubes (SWCNTs) embedded in a viscoelastic medium (layer) in a three-dimensional magnetic-thermal environment.

Objective

The most importantobjective of this study is to investigate the presence of possibility of coupling between transverse and torsional vibrations for circular symmetric cross sectionSWCNT.

Method

The equations are derived such that the circular cross-sectional area of the SWCNTs does not results in decoupling the transverse andtorsional motions. The nonlocal theory is used to take into account the small size effect of the SWCNTs. The deformations are described by bending slope angleand twisting angle using Euler angles. Considering the higher nonlinear terms causes the coupling the transverse and torsional motions.

Conclusions

Theresults show that a torsional initial motion causes not only a torsional motion but also a transverse motion. At the high (elevated) temperatures, the transverseoscillations decrease in a coupled mode. Transverse and torsional frequencies affect each other in a coupled mode. The amplitude of the transverse oscillationsdepends on the values of various parameters including the temperature, value of damping constants, and boundary conditions, etc. The SWCNTs aresurrounded by a layer (viscoelastic medium) having transverse and torsional elastic and damping behaviors. The torsional frequencies remain constant for anyvalues of the stiffness of layer in the transverse direction. But torsional frequencies increase by increasing the torsional stiffness of the viscoelastic layer,because it applies a twisting moment to the nanotube. But the transverse frequencies will not change by changing the torsional stiffness of viscoelasticmedium. As the torsional damping constant of viscoelastic layer increases, the oscillations in the transverse and torsional directions decrease faster andbecome damped. For different values of the damping constants in the torsional direction, the amplitude of the torsional oscillations is the same at thebeginning and then with the passage of time, a higher value of the damping constant compared to a lower damping constant, causes a more reduction of theoscillation amplitude in the torsional direction.