Abstract
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.
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