Transverse Wave Propagating In Carbon Nanotubes Under Multi-physics Fields Based On Generalized Gradient High-order Beam Theory

Carbon nanotubes(CNTs)are widely used in nano electromechanical system,composite materials and medical imaging.CNTs are considered as one of the crucial core components in nano electromechanical system,thus,it is of great importance to analyze CNTs'physical and mechanical performance.In this paper,an accurate and effective generalized gradient high-order beam theoretical model is established to study the transverse wave propagating in CNTs in the following three cases:Firstly,the transverse waves propagating in CNTs in free space is investigated based on the generalized gradient high-order beam theory model which is established in this paper.Then the governing equations of high-order beams based on nonlocal elasticity theory,strain gradient nonlocal elasticity theory and generalized strain gradient elasticity theory are established,respectively.And the corresponding dispersion of transverse waves in single-walled carbon nanotubes(SWCNT)and multi-walled carbon nanotubes(MWCNT)are deduced in detail.The influence of scale effect and van der Waals force on the wave speed of CNTs are discussed.The results of this paper have a good agreement with those from molecular dynamics simulation,which demonstrates that the wave behaviors of CNTs can be correctly described by the presented model.Secondly,the transverse waves propagating in CNTs under force-magnetic coupling is studied.CNTs is modelled as a generalized gradient high-order shear beam.A longitudinal magnetic field is exerted on CNTs,and CNTs'wave governing equations in this case is derived.The expression for frequency and phase velocity of transverse waves in SWCNT and MWCNT are given.The results show that the transverse wave propagating in CNTs can be obviously promoted by the magnetic field intensity.The wave speed is proportional to magnetic field intensity.If the magnetic field intensity increases from 0 to 2×10~8 A/m,the wave speed of CNTs can be increased by 24%.Finally,the transverse waves problems of CNTs embedded in elastic medium under force-magnetic coupling is studied,CNTs is modeled as a generalized gradient high-order shear beam theory model,and the elastic medium is simulated by a bi-parameter Pasternak substrate.The intensity and conductive properties of composite materials can be enhanced by adding CNTs(elastic modulus is up to 1 TPa),compared with CNTs,the surrounding environment can be considered as an elastic medium.The explicit expressions for cut-off frequency and phase velocity are derived,and the effects of magnetic field intensity and elastic medium on the wave behaviors of CNTs are analyzed.The numerical results indicate that the increase of the magnetic field intensity and surrounding elastic medium will result in a growing wave speed,which is related to the application performance of composite material.Research shows we can control the wave mode of CNTs by changing the external environment of CNTs to achieve the desired performance of nanodevices,which can contribute to the design of nano-sensors,high frequency nano-resonators and semiconductors nanocomposite.