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IssuesArchive of Issues2013-6pp.673-681

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N.A. Veklich, "Equation of Small Transverse Vibrations of an Elastic Pipeline Filled with a Transported Fluid," Mech. Solids. 48 (6), 673-681 (2013)
Year 2013 Volume 48 Number 6 Pages 673-681
DOI 10.3103/S0025654413060101
Title Equation of Small Transverse Vibrations of an Elastic Pipeline Filled with a Transported Fluid
Author(s) N.A. Veklich (Gubkin Russian State University of Oil and Gas, Leninskii pr-t 65, Moscow, 119991 Russia, vna@gubkin.ru)
Abstract The integro-differential equation of small transverse vibrations of a rectilinear elastic pipeline filled with a transported fluid is obtained. The pipeline vibrations are described in the linear setting in the beam approximation. The mutual dynamic influence of motions of the pipeline and the filling fluid is taken into account. A complete trigonometric series method is presented for solving problems with various boundary and initial conditions for the pipeline deflection.
Keywords pipeline, beam, vibrations, fluid, flow, incompressibility, continuity, hydroelasticity, trigonometric series
References
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3.  V. M. Pisarevskii, V. A. Polyakov, A. D. Prokhorov, et al., Foundations of Technical Diagnostics, Part 1 (Izd-vo "Neft i Gas", Moscow, 1996) [in Russian].
4.  M. P. Paidoussis, Fluid-Structure Interactions. Slender Structures and Axial Flow, Vol. 1 (Acad. Press, London, 1998).
5.  V. F. Ovchinnikov and L. V. Smirnov, "Numerical-Analytic Study of Hydroelastic OscillationVibration of Cantilevered Pipeline," Probl. Prochn. Plastichn., No. 68, 38-44 (2006).
6.  S. V. Nesterov, L. D. Akulenko, and L. I. Korovina, "Transverse Vibrations of a Pipeline with Uniformly Moving Fluid," Dokl. Ross. Akad. Nauk 427 (6), 781-784 (2009) [Dokl. Phys. (Engl. Transl.) 54 (8), 402-405 (2009)].
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8.  L. I. Sedov, Continuum Mechanics, Vol. 2 (Nauka, Moscow, 1970) [in Russian].
9.  G. A. Grinberg, "A New Method for Solving Several Boundary-Value Problems for Equations of Mathematical Physics Admitting Separation of Variables," Izv. Akad. Nauk SSSR. Ser. Fiz. 10 (2), 141-168 (1946).
10.  N. A. Veklich, "Axisymmetric Problems of Impact of an Elastic Disk on Fluid," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 175-184 (1992) [Mech. Solids (Engl. Transl.)].
11.  G. M. Fikhtengolts, Course of Differential and Integral Calculus, Vol. 3 (Nauka, Moscow, 1969) [in Russian].
Received 29 March 2011
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