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).
References: 
  1. Peddieson J., Buchanan R., McNitt R. P. Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science, 2003, vol. 41, pp. 595–609. https://doi.org/10.1016/S0020-7225(02)00210-0
  2. Bazehhour B. G., Mousavi S. M., Farshidianfar A. Free vibration of high-speed rotating Timoshenko shaft with various boundary conditions: effect of centrifugally induced axial force. Archive of Applied Mechanics, 2014, vol. 84, iss. 12, pp. 1691–1700. https://doi.org/10.1007/s00419-013-0762-5
  3. Karlicic D., Kozic P., Pavlovic R. Flexural vibration and buckling analysis of single-walled carbon nanotubes using different gradient elasticity theories based on Reddy and Huu-Tai formulations. Journal of Theoretical and Applied Mechanics, 2015, vol. 53, iss. 1, pp. 217–233. https://doi.org/10.15632/jtam-pl.53.1.217
  4. Ivanova E. A., Morozov N. F., Semenov B. N., Firsova A. D. Determination of elastic moduli of nanostructures: Theoretical estimates and experimental techniques. Mechanics of Solids, 2005, vol. 40, iss. 4, pp. 60–68.
  5. Daneshmand F., Rafiei M., Mohebpour S. R, Heshmati M. Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory. Applied Mathematical Modelling, 2013, vol. 37, iss. 16–17, pp. 7983–8003. https://doi.org/10.1016/j.apm.2013.01.052
  6. Sarkisjan S. O., Farmanyan А. Zh. Mathematical model of micropolar anisotropic (orthotropic) elastic thin shells. PNRPU Mechanics Bulletin, 2011, iss 3, pp. 128–145 (in Russian). EDN: OFUQLD
  7. Taliercio A., Veber D. Torsion of elastic anisotropic micropolar cylindrical bars. European Journal of Mechanics – A/Solids, 2016. vol. 55, pp. 45–56. https://doi.org/10.1016/j.euromechsol.2015.08.006
  8. Zhou X., Wang L. Vibration and stability of micro-scale cylindrical shells conveying fluid based on modified couple stress theory. Micro and Nano Letters, 2012, vol. 7, iss. 7, pp. 679–684. https://doi.org/10.1049/mnl.2012.0184
  9. Safarpour H., Mohammadi K., Ghadiri M. Temperature-dependent vibration analysis of a FG viscoelastic cylindrical microshell under various thermal distribution via modified length scale parameter: A numerical solution. Journal of the Mechanical Behavior of Materials, 2017, vol. 26, iss. 1–2, pp. 9–24. https://doi.org/10.1515/jmbm-2017-0010
  10. Sahmani S., Ansari R., Gholami R., Darvizeh A. Dynamic stability analysis of functionally graded higher-order shear deformable microshells based on the modified couple stress elasticity theory. Composites: Part B, 2013, vol. 51, pp. 44–53. https://10.1016/j.compositesb.2013.02.037
  11. Krylova E. Yu., Papkova I. V., Sinichkina A. O., Yakovleva T. B., Krysko-yang V. A. Mathematical model of flexible dimension-dependent mesh plates. Journal of Physics: Conference Series, 2019, vol. 1210, art. 012073. https://doi.org/10.1088/1742-6596/1210/1/012073, EDN: VVUQIS
  12. Scheible D. V., Erbe A., Blick R. H. Evidence of a nanomechanical resonator being driven into chaotic response via the Ruelle – Takens route. Applied Physics Letters, 2002, vol. 81, pp. 1884–1886. https://doi.org/10.1063/1.1506790
  13. Eremeyev V. A. A nonlinear model of a mesh shell. Mechanics of Solids, 2018, vol. 53, iss. 4, pp. 464–469. https://doi.org/10.3103/S002565441804012X, EDN: LTJZSA
  14. Krylova E. Yu., Papkova I. V., Saltykova O. A., Krysko V. A. Features of complex vibrations of flexible micropolar mesh panels. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 1, pp. 48–59 (in Russian). https://doi.org/10.18500/1816-9791-2021-21-1-48-59, EDN: MYYGLY
  15. Sedighi H. M., Malikan M., Valipour A., Zur K. K. Nonlocal vibration of carbon/boron-nitride nano-hetero-structure in thermal and magnetic fields by means of nonlinear finite element method. Journal of Computational Design and Engineering, 2020, vol. 7, iss. 5, pp. 591–602. https://doi.org/10.1093/jcde/qwaa041
  16. Sedighi H. M. Divergence and flutter instability of magneto-thermo-elastic C-BN hetero-nanotubes conveying fluid. Acta Mechanica Sinica/Lixue Xuebao, 2020, vol. 36, iss. 2, pp. 381–396. https://doi.org/10.1007/s10409-019-00924-4
  17. Panin V. E. Foundations of physical mesomechanics. Physical Mesomechanics, 1998, vol. 1, iss. 1, pp. 5–22 (in Russian). EDN: KWPHTL
  18. Glukhova O. E., Kirillova I. V., Kossovich E. L., Fadeev A. A. Mechanical properties study for graphene sheets of various size. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2012, vol. 12, iss. 4, pp. 63–66 (in Russian). https://doi.org/10.18500/1816-9791-2012-12-4-63-66, EDN: STJIYV
  19. Imran M., Hussain F., Khalil R. M. A., Sattar M. A, Mehboob H., Javid M. A., Rana A. M., Ahmad S. A. Anisotropic thermal and mechanical characteristics of graphene: A molecular dynamics study. Journal of Experimental and Theoretical Physics, 2019, vol. 128, iss. 2, pp. 259–267. https://doi.org/10.1134/S1063776119020079, EDN: DAUGJF
  20. Sargsyan S. H., Farmanyan A. J. Thermoelasticity of micropolar orthotropic thin shells. PNRPU Mechanics Bulletin, 2013, iss. 3, pp. 222–237 (in Russian). https://doi.org/10.15593/perm.mech/2013.3.222-237, EDN: RDKNJH
  21. Sheremetiev M. P., Pelekh B. L. To the construction of a refined theory of plates. Engineering Journal, 1964, vol. 3, iss. 3, pp. 34–41 (in Russian).
  22. Karman T. V. Festigkeitsprobleme im Maschinenbau. In: Klein F., Muller C. (eds.) Mechanik. Wies baden, Vieweg+Teubner Verlag, 1907, pp. 311–385. https://doi.org/10.1007/978-3-663-16028-1_5
  23. Erofeev V. I. Volnovye protsessy v tverdykh telakh s mikrostrukturoy [Wave Processes in Solids with Microstructure]. Moscow, Moscow University Press, 1999. 328 p. (in Russian).
  24. Volmir A. C. Nelineynaya dinamika plastin i obolochek [Nonlinear Dynamics of Plates and Shells]. Moscow, Nauka, 1972. 432 p. (in Russian).
  25. Hamilton W. Report of the Fourth Meeting. In: British Association for the Advancement of Science, London, 1835, pp. 513–518.
  26. Оstrоgradskу M. Memoires de l’Academie imperiale des sciences de St.-Petersbourg. St.-Petersbourg, L’Impr. de l’Academie imperiale des sciences , 1850, vol. 8, iss. 3, pp. 33–48.
  27. Sun C. T., Zhang Y. Size-dependent elastic moduli of platelike nanomaterials. Journal of Applied Physics, 2003, vol. 93, iss. 2, pp. 1212–1218. https://doi.org/10.1063/1.1530365
  28. Pshenichnov G. I. Teoriya tonkikh uprugikh setchatykh obolochek i plastinok [Theory of Thin Elastic Mesh Shells and Plates]. Moscow, Nauka, 1982. 352 p. (in Russian).
  29. Krysko V. A., Awrejcewicz J., Komarov S. A. Nonlinear deformations of spherical panels subjected to transversal load action. Computer Methods in Applied Mechanics and Engineering, 2005, vol. 194, iss. 27–29, pp. 3108–3126. https://doi.org/10.1016/j.cma.2004.08.005
  30. Schelling P. K., Keblinski P. Thermal expansion of carbon structures. Physical Review B, 2003, vol. 68, iss. 3, art. 035425. https://doi.org/10.1103/PhysRevB.68.035425
Received: 
12.10.2022
Accepted: 
19.09.2023
Published: 
31.05.2024
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