Dynamics and stability of a flexible pinned-free cylinder in axial flow

• A linear model has been developed for the dynamics of a cylinder flexibly supported only at the upstream end in axial flow.
• A pinned-free cylinder may lose stability by yawing/divergence at low flow velocities and by flutter at higher flows.
• For long pinned-free cylinders, increasing the length of the cylinder affects the stability of the system only weakly.

In this paper, the extended Hamilton׳s principle is used to obtain the linear equation of motion and boundary conditions for a cylinder flexibly supported by a translational and a rotational spring at the upstream end and free at the other, and subjected to axial flow. The equation of motion is solved numerically via Galerkin׳s method for a system in which the stiffness of the translational spring is infinitely large, while that of the rotational spring is zero, i.e. a pinned-free cylinder. For such a system, the condition for occurrence of non-oscillatory rigid-body instability is obtained analytically. Also, the Adomian Decomposition Method is used to obtain the critical flow velocity for divergence of pinned-free cylinders analytically. Finally, previously obtained experimental results for pinned-free cylinders are compared with those obtained numerically using the present theory.