Effects of surface roughness on the stability and dynamics of microtubes conveying internal fluid

Abstract

In this article, the instability and dynamic characteristics of fluid-conveying microtubes with surface roughness are studied. A theoretical model is presented to describe the dynamic behaviors of rough microtubes by introducing correction factors, which account for the effects of the surface roughness both on the structure and the internal fluid. The results demonstrate that the surface roughness has little effect on the correction factors for structure, but dramatically decreases the correction factors for fluid, which indicates that the Coriolis force and centripetal force caused by the internal fluid are reduced. For clamped–clamped microtubes, the surface roughness makes the nondimensional critical velocity for divergence and the natural frequency increase. And as the roughness height or the wave number increases, both the critical velocity and the frequency increase. For cantilevered microtubes, the critical velocity for fluttering depends on the surface roughness and the mass ratio. Curves describing the relationship between the nondimensional critical velocity $\hat{U}_{\text{cr}}$ and the mass ratio $\beta$ for smooth and rough microtubes are presented. Each curve contains a S-shaped segment, which is associated with the instability–restabilization–instability sequence. The surface roughness induces the curve shifting to the upper right of the $\hat{U}_{\text{cr}}$ − $\beta$ plane. In the region far away from the S-shaped segment, the critical velocity increases with the increasing of roughness height. And in the vicinity of S-shaped segment, the critical velocity for the rough microtube may be less than the value for the smooth microtube because of the sharply varying of critical velocity with mass ratio. The effects of surface roughness on the frequency of cantilevered microtubes are also analyzed and discussed.