Dynamic stability of a flexible spinning cylinder partially filled with liquid

Dynamic stability of a flexible spinning cavity cylinder partially filled with liquid is discussed in the paper The cylinder is assumed to be slender Choosing characteristic quantities and estimating the orders of magnitude of all terms in the governing equations and boundary conditions, the three-dimensional flow in the slender cylinder is reduced to a quasi-two-dimensional flow, Using the known formulas of a two-dimensional dynamic force acting on the rotor and regarding the slender cylinder as a Bernoulli-Euler beam, the perturbed equations of the liquid-filled beam-wise cylinder are derived. The analytical stability criteria as well as the stability boundaries are obtained. The results further the study of this problem.