Stabilization control of unstable vibration in a collapsible tube

When a collapsible tube or very flexible, thin-wall tube is used for conveying liquid, the tube happens to vibrate so severely in association with flow oscillation due to a large deformation of the tube's cross section. The vibration holds several modes depending on the liquid-flow rate and the deformation rate of tube cross-section, and the most significant vibration is a fundamental mode with a low frequency. This paper deals with experimental study to clarify the effects of active feedback control on the suppression of the unstable vibration occuring in the collapsible tube. The control pressure generated in proportion to the oscillating pressure and its derivative is feed-backed to the liquid flow in the tube, and we have found that the control pressure should be out-of-phase to the oscillating flow rate up to 50% of the onset flow rate of the case of the unstable vibration. Linear stability analyis of the control system can offer a rather good prediction to the phase angle of the pressure control but understimates the stability boundary in causing the tube deformation, which is not coincided with the experimental result.