In this paper, Lagrange's equations along with the Ritz method are used to obtain the equation of motion for a flexible, slender cylinder subjected to axial flow. The cylinder is supported only by a translational and a rotational spring at the upstream end, and at the free end, it is terminated by a tapering end-piece. The equation of motion is solved numerically for a system in which the translational spring is infinitely stiff, thus acting as a pin, while the stiffness of the rotational spring is generally non-zero. The dynamics of such a system with the rotational spring of an average stiffness is described briefly. Moreover, the effects of the length of the cylinder and the shape of the end-piece on the critical flow velocities and the modal shapes of the unstable modes are investigated.
IntroductionSince the study by Hawthorne [1] in the late 1950s on the dynamics of the Dracone, a flexible sausage-like container towed behind a small vessel, the dynamics and stability of flexible slender structures subjected to axial flow have been studied extensively by applied mechanics researchers; some examples are the studies by Païdoussis [2-4] on the dynamics of flexible cylinders in axial flow with various boundary conditions, the studies by Triantafyllou and Chryssostomidis [5,6] on the dynamics of a cantilevered beam and a pinned-free string subjected to axial flow, and those by Dowling [7,8] on the dynamics of neutrally and negatively buoyant elements of a towed system; for a comprehensive review of these studies, see [9].