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Mathematical Modeling of Hydroelastic Oscillations of Circular Sandwich Plate Resting on Winkler Foundation

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Recent Research in Control Engineering and Decision Making (ICIT 2020)

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 337))

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Abstract

Modern composite materials consist of layers with different physical properties. Three-layered composite plates or sandwich plates are widely used in aerospace industry and civil engineering. However, the issues of hydroelastic vibrations of these plates resting on an elastic foundation are not well studied. We investigated the mathematical modeling problem of hydroelastic oscillations for a three-layered circular plate interacting with pulsating viscous liquid layer. The sandwich plate was mounted on Winkler foundation and forms the bottom wall of the narrow channel. The upper wall of the narrow channel was an absolutely rigid disk. The disk and plate were coaxial and parallel to each other. The channel was filled with a pulsating viscous incompressible liquid. The plate’s kinematics was considered within the framework of the broken normal hypothesis. The radial and bending vibrations of the plate were studied on the basis of the formulation and solution of the coupled hydroelasticity problem. The hydroelasticity problem includes the dynamics equations of the plate, the dynamics equations of the liquid layer and corresponding boundary conditions. Using the perturbation method, we solved the formulated hydroelasticity problem. Using the obtained solution, we constructed and investigated frequency-dependent distribution functions of sandwich plate’s displacements. These functions allowed us to determine the resonant frequencies for radial and bending vibrations of a three-layered circular plate.

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Acknowledgments

The study was funded by Russian Foundation for Basic Research (RFBR) according to the projects № 18-01-00127-a and № 19-01-00014-a.

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Authors and Affiliations

  1. Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya Street, Saratov, 410054, Russia

    Aleksandr Chernenko, Lev Mogilevich, Victor Popov & Anna Popova

  2. Saratov State University, 83 Astrakhanskaya Street, Saratov, 410012, Russia

    Alevtina Christoforova

Authors
  1. Aleksandr Chernenko
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  2. Alevtina Christoforova
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  3. Lev Mogilevich
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  4. Victor Popov
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  5. Anna Popova
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Corresponding author

Correspondence to Victor Popov .

Editor information

Editors and Affiliations

  1. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Olga Dolinina

  2. ITMO University, Saint Petersburg, Russia

    Igor Bessmertny

  3. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Alexander Brovko

  4. University of Texas at El Paso, El Paso, USA

    Vladik Kreinovich

  5. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Vitaly Pechenkin

  6. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Alexey Lvov

  7. Novosibirsk State Technical University, Novosibirsk, Russia

    Vadim Zhmud

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Chernenko, A., Christoforova, A., Mogilevich, L., Popov, V., Popova, A. (2021). Mathematical Modeling of Hydroelastic Oscillations of Circular Sandwich Plate Resting on Winkler Foundation. In: Dolinina, O., et al. Recent Research in Control Engineering and Decision Making. ICIT 2020. Studies in Systems, Decision and Control, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-030-65283-8_8

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