Nonlinear vibration and stability analysis of axially loaded embedded carbon nanotubes conveying fluid

In this paper, for the first time, the influence of internal moving fluid and compressive axial load on the nonlinear vibration and stability of embedded carbon nanotubes is investigated. The Euler-Bernoulli beam theory is employed to model the vibrational behaviour of an embedded carbon nanotube. The relationship of nonlinear amplitude and frequency for single-wall nanotubes in the presence of internal fluid flow is expressed using the multiple scales perturbation method. The amplitude-frequency response curves of the nonlinear vibration obtained and the effects of the surrounding elastic medium, applied axial loads, mass and the aspect ratios of nanotubes are discussed. It is shown that beyond the critical flow velocity buckling occurs. The stability margins of the carbon nanotubes under combined hydroelastic and axial loadings are studied and it is shown that the surrounding elastic medium plays a significant role in the stability of the carbon nanotube.