The dynamics of clusters of flexible cylinders in axial flow: Theory and experiments

This paper presents an outline of the theory for the dynamics of clusters of independently supported flexible cylinders in axial flow, and an extensive discussion of the behaviour of such systems with increasing flow velocity, with special emphasis placed on the modal forms of free coupled motions of the cylinders and on the onset of instabilities. Results of an experimental study of the problem are also presented, involving systems of two, three or four cylinders supported at both ends and positioned symmetrically in the cylindrical test section of a water tunnel; experiments were conducted with different inter-cylinder gaps and support conditions. Both theory and experiment show that with increasing flow the system loses stability by buckling in one of its coupled modes, commonly in a pattern where cylinders move towards one another symmetrically, maximum displacement occurring just downstream of their midpoints. With increasing flow, theory predicts that other buckling instabilities are superimposed on the first; in the experiments the system remains buckled, changing modal patterns constantly; some of them correspond to those predicted by theory. At sufficiently high flow, oscillatory motion is observed, corresponding to theoretical flutter. Theory and experiment agree qualitatively in most essential features of the dynamical behaviour of the system, and quantitative agreement in the critical flow velocities for the onset of the first buckling instability is remarkably good.