Unstable Vibration of Simply Supported Thin Cylindrical Shells Subjected to Axial Leakage Flows Using Flu¨gge’s Shell Theory

The unstable vibration of thin cylindrical shells subjected to axial leakage flows is investigated in this paper. Considering the fluid structure interaction between shells and fluids flowing through a narrow passage, the coupled equation of motion between shells and flowing fluids is derived using the Flu¨gge’s shell theory and the Navier-Stokes equation. Focusing on the vibrational characteristics of a thin cylindrical shell with both simply-supported ends, that are the axisymmetric vibration, the lateral vibration and the circumferential vibration, the unstable phenomenon of thin cylindrical shells are clarified by using the root locus based on the complex eigenvalue analysis. The numerical parameter studies on the shells with both simply-supported ends are performed taking the dimensions of shells, the characteristics of flowing fluids and the clearance of an annular gap as parameters. The influences of these parameters on the threshold of the instability of the coupled vibration between a shell and a flowing fluid are discussed.