Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Krylova E. Y. Mathematical model of orthotropic meshed micropolar cylindrical shells oscillations under temperature effects. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 2, pp. 231-244. DOI: 10.18500/1816-9791-2024-24-2-231-244, EDN: VLEBOS

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.05.2024
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
539.3
DOI: 
10.18500/1816-9791-2024-24-2-231-244
EDN: 
VLEBOS

Mathematical model of orthotropic meshed micropolar cylindrical shells oscillations under temperature effects

Autors: 
Krylova Ekaterina Yu., Saratov State University
Abstract: 

In the work the mathematical model of micropolar meshed cylindrical shells oscillations under the action of the vibrational and temperature effects is constructed. The shell material is an elastic orthotropic homogeneous Cosserat pseudocontinuum with constrained rotation of particles. The Duhamel – Neumann’s law was adopted. The mesh structure is taken into account according to the model of G. I. Pshenichnov, geometric nonlinearity according to Theodor von Karman theory. The equations of motion, boundary and initial conditions are obtained from the Ostrogradsky – Hamilton variational principle based on the Tymoshenko kinematic model. The constructed a mathematical model will be useful, among other things, in the study of the behavior of carbon nanotubes under various operating conditions.

Key words: 
mesh structure cylindrical shells
mathematical modeling
thermodynamics
carbon nanotube
Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 22-21-00331).
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Received: 
12.10.2022
Accepted: 
19.09.2023
Published: 
31.05.2024
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