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A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2025-2pp.965-972

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A.G. Khakimov and A.A. Yulmukhametov, "Bending Vibrations of a Pipeline on Elastic Supports with Moving Liquid," Mech. Solids. 60 (2), 965-972 (2025)
Year 2025 Volume 60 Number 2 Pages 965-972
DOI 10.1134/S002565442560031X
Title Bending Vibrations of a Pipeline on Elastic Supports with Moving Liquid
Author(s) A.G. Khakimov (Mavlyutov Institute of Mechanics UFRC RAS, Ufa, 450054 Russia, hakimov@anrb.ru)
A.A. Yulmukhametov (Mavlyutov Institute of Mechanics UFRC RAS, Ufa, 450054 Russia, artyr_yulmuhametov@mail.ru)
Abstract The natural bending vibrations of a pipeline are investigated. It is assumed that the parts of the pipeline on both sides of the sagging section have elastic supports. It is assumed that a constant longitudinal force acts along the neutral line. An incompressible liquid flows through the pipe with a constant average velocity. The effect of the internal pressure in the pipe on these vibrations is taken into account. The direct and inverse problems are solved. The speed parameter, the mass of liquid per unit length of the pipeline, and the dimensionless mass flow rate of liquid through the pipeline can be determined from two frequencies of bending vibrations.
Keywords pipeline, elastic supports, bending vibrations, natural frequencies, internal pressure, fluid velocity, direct and inverse problems
Received 17 January 2025Revised 17 February 2025Accepted 18 February 2025
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