Non-axisymmetric coupled non-stationary problem of thermoelectroelasticity for a long piezoceramic cylinder

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

A new closed solution to the non-axisymmetric coupled non-stationary problem of thermoelectroelasticity was constructed for a long piezoceramic cylinder for the case of satisfaction of the first and the third kind boundary conditions. Cylindrical surfaces were made as electrodes and connected to a measurement device with large input resistance. Limitation of a temperature change “load” rate made it possible to include equations of statics, electrostatics and thermal conductivity in the initial formula. The finite biorthogonal transforms are applying to explore a non-selfadjoint system of differential equations and to develop a closed solution. The obtained relations made it possible to determine the temperature and electric fields, and the stress-strain state in the piezoceramic cylinder, as well as the potential difference between cylindrical surfaces (electrodes) under non-stationary non-axisymmetric temperature impact.

About the authors

D. A. Shlyahin

Samara Polytech

Author for correspondence.
Email: d-612-mit2009@yandex.ru
Russian Federation, Samara

V. A. Jurin

Samara Polytech

Email: get8ack@mail.ru
Russian Federation, Samara

References

  1. Ionov B.P., Ionov A.B. Statistic-spectral approach to noncontact temperature measurement // Sensors and Systems. 2009. V. 2. P. 9–11.
  2. Kazaryan A.A. Fine-film captive pressure and temperature // Sensors and Systems. 2016. V. 3. P. 50–56.
  3. Pan’kov A.A. Resonant diagnostics of temperature distribution by the piezo-electro-luminescent fiber-optical sensor according to the solution of the Fredholm integral equation // PNRPU Mechanics Bulletin. 2018. V. 2. P. 72–82; https://doi.org/10.15593/perm.mech/2018.2.07.
  4. Kalmova M. The scope of application of devices whose operation is based on taking into account the connectivity of thermoelectroelastic fields // Austrian Journal of Technical and Natural Sciences. 2022. V. 3. № 4. P. 14–16; https://doi.org/10.29013/AJT-22-3.4-14-16.
  5. Mindlin R.D. Equations of high frequency vibrations of thermopiezoelectric crystal plates // International Journal of Solids and Structures. 1974. V. 10. № 6. P. 625–637; https://doi.org/10.1016/0020-7683(74)90047-X.
  6. Lord H.W., Shulman Y. A generalized dynamical theory of thermoelasticity // J. Mech. Phys. Solids. 1967. V. 15. № 5. P. 299–309; https://doi.org/10.1016/0022-5096(67)90024-5.
  7. Green A.E., Naghdi P.M. Thermoelasticity without energy dissipation // J. Elasticity. 1993. V. 31. P. 189–208.
  8. Vatulyan A.O., Nesterov S.A. The dynamic problem of thermoelectroelasticity for functionally graded layer // Computational Continuum Mechnics. 2017. V. 2. № 10. P. 117–126; https://doi.org/10.7242/1999-6691/2017.10.2.10.
  9. Babeshko V.A., Ratner S.V., Syromyatnikov P.V. On mixed problems for thermoelectroelastic media with discontinuous boundary conditions // Doklady Physics. 2007. V. 52. P. 90–95; https://doi.org/10.1134/S102833580702005X.
  10. Saadatfar M., Razavi A.S. Piezoelectric hollow cylinder with thermal gradient // J. Mech. Sci. Technol. 2009. V. 23. P. 45–53; https://doi.org/10.1007/s12206-008-1002-8.
  11. Akbarzadeh A.H., Babaei M.H., Chen Z.T. The thermo-electromagnetoelastic behavior of a rotating functionally graded piezoelectric cylinder // Smart Materials and Structures. 2011. V. 20. № 6; https://doi.org/10.1088/0964-1726/20/6/065008.
  12. Rahimi G.H., Arefi M., Khoshgoftar M.J. Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads // Appl. Math. Mech. 2011. V. 32. № 8. P. 997–1008; https://doi.org/10.1007/s10483-011-1475-6.
  13. Shlyakhin D.A., Kal’mova M.A. The coupled non-stationary thermo-electro-elasticity problem for a long hollow cylinder // Journal of Samara State Technical University. Ser. Physical and Mathematical Sciences. 2020. V. 4. № 14. P. 677–691; https://doi.org/10.14498/vsgtu1781.
  14. Shlyakhin D.A., Kal’mova M.A. The nonstationary thermoelectric elasticity problem for a long piezoceramic cylinder // PNRPU Mechanics Bulletin. 2021. V. 2. P. 181–190; https://doi.org/10.15593/perm.mech/2021.2.16.
  15. Shlyakhin D.A., Kal’mova M.A. Related dynamic axisymmetric thermoelectroelasticity problem for a long hollow piezoceramic cylinder // Advanced Engineering Research (Rostov-on-Don). 2022. V. 2. № 22. P. 81–90; https://doi.org/10.23947/2687-1653-2022-22-2-81-90.
  16. Dai H.L., Wang X, Dai Q.H. Thermoelectroelastic responses in orthotropic piezoelectric hollow cylinders subjected to thermal shock and electric excitation // J. Reinfor. Plast. Comp. 2005. V. 24. № 10. P. 1085–1103; https://doi.org/10.1177/0731684405048834.
  17. Dai H.L., Wang X. Thermo-electro-elastic transient responses in piezoelectric hollow structures // Int. J. Solids Struct. 2005. V. 42. № 3–4. P. 1151–1171; https://doi.org/10.1016/j.ijsolstr.2004.06.061.
  18. Obata Y., Noda N. Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material // J. Therm. Stresses. 1994. V. 17. № 3. P. 471–487; https://doi.org/10.1080/01495739408946273.
  19. Chen W.Q., Shioya T. Piezothermoelastic behavior of a pyroelectric spherical shell // J. Therm. Stresses. 2001. V. 24. P. 105–120; https://doi.org/10.1080/01495730150500424.
  20. Jabbari M., Sohrabpour S., Eslami M.R. General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to non-axisymmetric steady-state loads // J. Appl. Mech. 2003. V. 70. № 1. P. 111–118; https://doi.org/10.1115/1.1509484.
  21. Atrian A., Fesharaki J.J., Majzoobi G.H., Sheidaee M. Effects of electric potential on thermo-mechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads // Int. J. Mech., Aerospace, Indust., Mech. Manufac. Eng. 2011. V. 5. № 11. P. 2441–2444; https://doi.org/10.5281/zenodo.1060363.
  22. Dai H.L., Luo W.F., Dai T., Luo W.F. Exact solution of thermoelectroelastic behavior of a fluid-filled FGPM cylindrical thin-shell // Compos. Struct. 2017. V. 162. P. 411–423; https://doi.org/10.1016/j.compstruct.2016.12.002.
  23. Ishihara M., Ootao Y., Kameo Y. A general solution technique for electroelastic fields in piezoelectric bodies with D∞ symmetry in cylindrical coordinates // J. Wood Sci. 2016. V. 62. P. 29–41; https://doi.org/10.1007/s10086-015-1524-5.
  24. Ishihara M., Ootao Y., Kameo Y. Analytical technique for thermoelectroelastic field in piezoelectric bodies with D∞ symmetry in cylindrical coordinates // J. Therm. Stresses. 2017. V. 41. № 6. P. 1–20; https://doi.org/10.1080/01495739.2017.1368052.
  25. Shlyakhin D.A., Yurin V.A. Non-axisymmetric non-stationary problem of thermoelectroelasticity for a long piezoceramic cylinder // Eng. J.: Sci. Innov. 2023. V. 7. P. 677–691; https://doi.org/10.18698/2308-6033-2023-7-2288.
  26. Kovalenko A.D. Fundamentals of Thermoelasticity. Kiev: Naukova Dumka, 1970. 307 p.
  27. Parton V.Z., Kudryavtsev B.A. Electromagnetoelasticity: Piezoelectrics and Electrically Conductive Solids. Moscow: Science, 1988, 470 p.
  28. Sneddon I.N. Fourier Transforms. Moscow: Foreign Literature, 1955. 668 p.
  29. Senitsky Y.E. Study of the Elastic Deformations of Structural Elements Under Dynamic Influences by the Method of Finite Integral Transformations. Saratov. Saratov University, 1985. 174 p.
  30. Yanke E., Emde F., Lesh F. Special functions. Moscow: Science, 1977. 342 p.
  31. Hong C.H., Kim H.P., Choi B.Y. et al. Lead-free piezoceramics – Where to move on? // J. Materiomics. 2016. V. 2. № 1. P. 1–24; https://doi.org/10.1016/j.jmat.2015.12.002

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2024 Russian Academy of Sciences