For citation:
Krysko A. V., Krechin A. N., Zhigalov M. V., Krysko V. A. Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 4, pp. 587-597. DOI: 10.18500/1816-9791-2024-24-4-587-597, EDN: ZFBSON
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
25.11.2024
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Russian
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Article
UDC:
539.3
EDN:
ZFBSON
Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts
Autors:
Krysko Anton V., Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences
Krechin Alexander N., Yuri Gagarin State Technical University of Saratov
Zhigalov Maxim Viktorovich, Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences
Krysko Vadim A., Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences
Abstract:
In this paper, nonlinear mathematical models of functionally gradient porous nanobeams are constructed taking into account transverse shifts. Transverse shifts are described using kinematic models of the second (S. P. Timoshenko) and third approximations (Sheremetyev – Pelekh). From the Sheremetyev – Pelekh model, as a special case, the kinematic models of the second (S. P. Timoshenko) and first approximation (Bernoulli – Euler) follow. Geometric nonlinearity is accepted according to T. von Karman, nanoeffects are accepted according to the modified Yang moment theory of elasticity. The required equations are derived from the Ostrogradsky – Hamilton principle. An efficient algorithm has been developed that allows us to consider both static and chaotic dynamics problems. Numerical examples are given.
Key words:
Acknowledgments:
The research was carried out at the expense of a grant from the Russian Science Foundation (project No. 22-11-00160).
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Received:
20.06.2023
Accepted:
03.07.2023
Published:
29.11.2024
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