We study specific features of the behavior of a straight pipeline in the case where the velocity of flowing liquid varies within the subcritical or supercritical range. On the basis of a model that takes into account four modes of vibration and the Coriolis force, we study the ranges of stability of vibrations of the straight pipeline. We discover new dynamical modes of the behavior of pipeline in the supercritical case. The numerical simulation performed within the framework of the 12-mode model confirms the obtained qualitative results. We also reveal the specific character of the action of the Coriolis force for supercritical modes of the flow of liquid in the pipeline.
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Yu. E. Vasilevskii and O. S. Limarchenko, “Nonlinear model of the dynamics of pipelines with high-speed flows of liquid,” in: Complex Analysis and Flows with Free Boundaries, Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, 2, No 4 (2006), pp. 322–334.
O. Lymarchenko and O. Timokhin, “Dynamic behavior of a pipeline with free end in the vicinity of critical velocities of motion of liquid,” Fiz.-Mat. Model. Inform. Tekhnol., No. 14, 73–77 (2011).
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Translated from Neliniini Kolyvannya, Vol. 19, No. 2, pp. 235–239, April–June, 2016.
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Limarchenko, O.S., Timokhin, A.P. Specific Features of the Dynamic Behavior of a Straight Pipeline for Supercritical Velocities of the Flow of Liquid. J Math Sci 223, 293–297 (2017). https://doi.org/10.1007/s10958-017-3355-y
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DOI: https://doi.org/10.1007/s10958-017-3355-y