Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale

Based on theory of nonlocal elasticity, a nonlocal double-elastic beam model is developed for the vibration analysis of double-walled carbon nanotubes (DWCNTs) conveying fluid. The effect of small length scale is incorporated in the formulation. The natural frequency and critical flow velocity for the case of simply supported DWCNTs conveying fluid are obtained. The effect of small length scale on the properties of vibration and instability is discussed. It is demonstrated that the natural frequencies of DWCNTs conveying fluid are dependent upon the small length scale. However, the effect of small length scale on the critical flow velocities can be neglected.