Flexural vibrations of microscale pipes conveying fluid by considering the size effects of micro-flow and micro-structure

In this paper, the in-plane and out-of-plane flexural vibrations of microscale pipes conveying fluid with clamped–clamped ends are examined theoretically, by modifying the classical equations of motion with consideration of the size effects of micro-flow and micro-structure. The theoretical model including an additional parameter associated with the flow velocity profile and another material length scale parameter representing the size effect of micro-structure is valid for both straight and curved pipe systems. The results of calculating the evolution of natural frequencies for straight pipes with increasing mean flow velocity show that the material length scale parameter tends to stiffer the microscale pipe and hence increases the critical flow velocity while the parameter describing the effect of flow velocity profile would decrease the critical flow velocity. For curved pipes, however, the modified inextensible theory predicts that the effect of micro-flow on the in-plane and out-of-plane natural frequencies may be not visible.