Fluid passing through a cylindrical shell causes both lateral displacements and deformation of the cross-section. Studies have shown that this applies to both the cantilevered and clamped-clamped shells. The effect of boundary conditions was examined and it was concluded that a system with identical end conditions (clamped or pinned) is conservative; thus, at sufficiently high flow, it loses stability by divergence, followed by coupled-mode flutter at a slightly higher flow velocity. This thesis focuses on the systems of clamped-pinned and pinned-clamped shells. Initially using two different theories, the standing wave analysis and the travelling wave analysis, small dampings (negative or positive) are found in a system of clamped-pinned (and pinned-clamped) ends before the flow reaches the critical divergence velocity. The same result is obtained based on an analysis of an elastically constrained shell. Upon further examination, it is found that the small dampings observed in the first two cases are simply numerical artifacts: the magnitude of these dampings tends to zero as the accuracy of the computation is improved Hence, it is concluded that the clamped-pinned and pinned-clamped systems are conservative.

Paidoussis, Michael P. (Supervisor)

Misra, A. K. (Supervisor)