Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts

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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. 

Sobre autores

Anton Krysko

Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences

Email: anton.krysko@gmail.com
ORCID ID: 0000-0002-9389-5602
Código SPIN: 3862-0430
15 Lavrentiev Ave., Novosibirsk 630090, Russia

Alexander Krechin

Yuri Gagarin State Technical University of Saratov

Email: san9.antonov@yandex.ru
Código SPIN: 9228-8100
Russia, 410054, Saratov, Politekhnicheskaya st., 77

Maxim Zhigalov

Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences

Email: zhigalovm@yandex.ru
ORCID ID: 0000-0002-0642-7211
Código SPIN: 5055-2568
Scopus Author ID: 25923214900
Researcher ID: AAB-7146-2021
15 Lavrentiev Ave., Novosibirsk 630090, Russia

Vadim Krysko

Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences

Autor responsável pela correspondência
Email: tak@san.ru
ORCID ID: 0000-0002-4914-764X
Código SPIN: 1024-5028
15 Lavrentiev Ave., Novosibirsk 630090, Russia

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