@ARTICLE{Kheiri_Mojtaba_Dynamics_2016, author={Kheiri, Mojtaba}, volume={vol. 63}, number={No 3}, journal={Archive of Mechanical Engineering}, pages={379-396}, howpublished={online}, year={2016}, publisher={Polish Academy of Sciences, Committee on Machine Building}, abstract={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.}, type={Artykuły / Articles}, title={Dynamics and stability of a flexible, slender cylinder flexibly restrained at one end and free at the other and subjected to axial flow}, URL={http://www.czasopisma.pan.pl/Content/104266/PDF/ame-2016-0022.pdf}, doi={10.1515/meceng-2016-0022}, keywords={dynamics, axial flow, cylinder, pinned-free, Lagrange's equations}, }