Mathematical modeling of three-layer beam hydroelastic oscillations

L. I. Mogilevich1 , V. S. Popov2 , A. A. Popova3 , A. V. Christoforova4 , E. V. Popova5

1, 2, 3Yuri Gagarin State Technical University of Saratov, Saratov, Russia

4, 5Saratov State University, Saratov, Russia

2Corresponding author

Vibroengineering PROCEDIA, Vol. 12, 2017, p. 12-18. https://doi.org/10.21595/vp.2017.18462
Received 11 April 2017; accepted 12 April 2017; published 30 June 2017

Copyright © 2017 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract.

The problem of hydroelastic oscillations of three-layer beam interacting with viscous liquid layer is set up and analytically solved. The problem presents the equation system of a three-layer beam and Navier-Stokes equations. The following boundary conditions are chosen: the no-slip conditions, the conditions for pressure at the edges, the simply supported edges conditions. The problem is solved for the steady-state harmonic regime. The frequency dependent distribution functions of the beam deflection are constructed. The given function allows investigating the resonance hydroelastic oscillations of a three-layer beam, as well as its deflected mode.

Keywords: hydroelasticity, vibration, three-layer beam, viscous liquid, mathematical modeling.

Acknowledgements

The study was funded by Russian Foundation for Basic Research (RFBR) according to the Projects Nos. 15-01-01604-a, 16-01-00175-a and President of Russian Federation Grant No. MD-6012.2016.8.

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