Instability of an Axial Annular Flow-Induced Vibration of Thin Cylindrical Shells Having Freely Supported End

Abstract

When thin cylindrical shells having freely supported end such as heat-shielding shells of after-burners, labyrinth air seals and annular structures in large diameter pipings are subjected to axial annular flow, an unstable vibration and a fatigue failure are apt to be occurred. In this paper, the unstable vibration of thin cylindrical shells is investigated cconsidering the fluid structure interaction between shells and fluid flowing through a narrow passage. The coupled equation of motion between shells and fluid is derived using Flügge's shell theory and Navier-Stokes equation. Especially, focusing on the higher circumferential vibrations, the unstable phenomenon of thin cylindrical shells is clarified by using root locus based on the complex eigenvalue analysis by using the mode functions obtained by the exact solution. The influence of shell-dimensions and so forth on the threshold of the instability of the coupled vibration of shells and flowing fluid are investigated and discussed.