Abstract
Based on the Timoshenko beam theory and Bernoulli-Fourier method, a single-elastic beam model is developed for transverse vibrations of single-walled carbon nanotubes under additional axial load, which includes the effects of the elastic medium around them. Explicit expressions are derived for the natural frequencies and transversal responses of simply supported single-walled carbon nanotubes. The influence of addition axial load and the properties of elastic medium on the vibrations are discussed. The results showed that the effects of addition axial load on the lower natural frequencies of single-walled carbon nanotubes are sensitive to the lower vibration modes and the stiff elastic medium. The lower natural frequencies depend on the axial load; they become smaller with increasing axial load and vary with the vibration modes. In addition, except for the first mode, the effects of the axial load on the stiff elastic medium are considerably greater than those on the flexible one. However, the constants of the elastic medium have little effect on the first mode. The critical axial buckling stress and strain for simply-supported single-walled carbon nanotubes are also obtained.
Highlights
Carbon nanotubes (CNT) are an exciting new material that has potential applications in nanobiological devices and nanomechanical systems
The results showed that the effects of addition axial load on the lower natural frequencies of single-walled carbon nanotubes are sensitive to the lower vibration modes and the stiff elastic medium
The main goal of this study is to analyze the transverse vibrations of single-walled carbon nanotubes (SWCNTs) which are modeled as a Timoshenko beam and embedded in an elastic medium
Summary
Carbon nanotubes (CNT) are an exciting new material that has potential applications in nanobiological devices and nanomechanical systems Due to their remarkable mechanical, physical, and chemical properties, carbon nanotubes may be used as fluid conveyers or potential reinforcements in nanocomposite materials [1-3]. Since experiments at the nanoscale are extremely difficult to conduct, theoretical modeling of the mechanical response of carbon nanotubes has been carried out [4,5]. These modeling approaches generally include atomistic modeling and continuum mechanics modeling. Several types of continuum-based elasticity theory, which model CNT as an elastic cylindrical tube, have been used to study the nanomechanics and vibration responses of CNT.
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