Dynamics of a Pipeline with a Liquid on a Rotating Base
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International Applied Mechanics, Vol. 56, No. 3, May, 2020
DYNAMICS OF A PIPELINE WITH A LIQUID ON A ROTATING BASE
V. O. Limarchenko, O. S. Limarchenko, and N. N. Sapon
A model of a pipeline that rotates about its longitudinal axis and in which a fluid flows is developed. A nonlinear finite-dimensional dynamic model of a pipeline with fluid is constructed in terms of amplitudes of vibration modes of a resting pipeline with fluid based on a nonlinear model that uses the mixed (Euler–Lagrangian) description of the motion of the elastic and liquid components and accounts for centrifugal forces, internal pressure forces, reactive forces, Coriolis forces, and longitudinal compression. The dependence of the vibration frequencies of the pipeline on the parameters of fluid motion and the angular velocity of the pipeline is studied. The sub- and supercritical ranges are established based on the critical velocities determined. The effect of the pulsation of flow velocities on the dynamical behavior of the pipeline both in sub- and supercritical ranges of fluid velocities is analyzed. It is shown that an increase of fluid velocity (both medium and pulsation components) leads to an increase of the frequencies and amplitudes of pipeline oscillations. Keywords: pipeline with fluid, rotation about longitudinal axis, pulsation of fluid velocity, dynamical behavior, critical velocity Introduction. Pipelines with a fluid flow are an integral part of many transport, power, and other systems. The predominant part of research on such objects is related to pipelines conveying compressed gas or high-pressure steam and cases where the base (fastening) of the pipeline is fixed. In the case of a pipeline with fluid, in contrast to the case of light steam, the inertial properties of the fluid cannot be neglected (the mass of the fluid and the pipeline per unit length become of the same order), which leads to the need to consider the associated hydroelastic problem [1, 2, 6–8, 12]. The motion in the pipeline–fluid system can be excited both by impulsive and vibration loads on the pipeline and its base. The behavior of a pipeline with a fluid flow during the rotation of the bearing base about the longitudinal axis of the pipeline in the presence of pulsations of the fluid velocity is considered for the first time. This type of problem is generated primarily by drilling technologies [4]. The work is based on the approaches [1, 2, 5, 6], where a the mixed (Euler–Lagrangian) description of the motion of the system components is developed and a discrete model of the system based on the method of modal decomposition is derived. The mathematical apparatus is based on the application of the formulation of the problem using the Hamilton–Ostrogradsky variational principle, the concept of amplitude, and spatial separation of motions (methods of nonlinear mechanics and variational methods of mathematical physics). Particular attention is paid to the behavior of the system in the vicinity of the critical velocities of the fluid flow when bifurcation mo
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