On the dynamic motion of a thin flexible cylinder in a viscous stream

The stability and time-dependent deflexions of a thin flexible cylinder with zero bending rigidity set in a viscous stream are examined. The cylinder is fixed at one end and free at the other. Modal shapes are found based on solutions to linearized equations resulting from small deflexion assumptions; the dependence of cylinder motion upon the aerodynamic, elastic and physical size characteristics of the cylinder is exhibited. It is found that the cylinder motion is always unstable and that cylinder amplitude increases without bound as time is increased.