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Effect of Hydrostatic Stress and Piezoelasticity in a Thermopiezoelectric Layer Resting on Gravitating Half Space with Slip Interface

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Advances in Fluid Dynamics

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

In this paper, an analytical model is developed to study the influence of initial hydrostatic stress and piezoelasticity on elastic waves in a thermopiezoelectric layer embedded on a gravitating half space with slip interface. The thermopiezoelectric layer considered for this study is hexagonal (6 mm) material. The problem is described using equations of linear elasticity with initial hydrostatic stress and piezothermoelastic inclusions. Displacement functions in terms of velocity potential are introduced to separate the motion’s equations, heat and electric conduction equations. The frequency equations are obtained by stress-free, insulated thermal and electrically shorted boundary conditions at the gravitating half space. The numerical computation is carried out for the PZT-4A material. The obtained results are presented graphically to show the effect of piezoelastic coupling and hydrostatic stress on the elastic waves.

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References

  1. Morse RW (1954) Compressional waves along an anisotropic circular cylinder having hexagonal symmetry. J Acoust Soc America 26:1018–1021. https://doi.org/10.1121/1.1907460

    Article  MathSciNet  Google Scholar 

  2. Bhimraddi AA (1984) A higher order theory for free vibration analysis of circular cylindrical shell. Int J Solid Struct 20:623–630. https://doi.org/10.1177/0731684407081385

    Article  Google Scholar 

  3. Mindlin RD (1979) Equation of high frequency vibrations of thermo-piezoelectric crystal plates. In: Interactions in elastics solids. Springer, Wien

    Google Scholar 

  4. Nowacki W (1978) Some general theorems of thermo-piezoelectricity. J Therm Stresses 1:171–182. https://doi.org/10.1080/01495737808926940

    Article  Google Scholar 

  5. Nowacki W (1979) Foundations of linear piezoelectricity. In: Parkus H (ed) Electromagnetic interactions in elastic solids. Springer, Wien. (Chapter 1)

    Google Scholar 

  6. Chandrasekhariah DS (1984) A temperature rate dependent theory of piezoelectricity. J Therm Stresses 7:293–306. https://doi.org/10.1080/01495738408942213

  7. Chandrasekhariah DS (1988) A generalized linear thermoelasticity theory of piezoelectric media. Acta Mech 71:39–49. https://doi.org/10.1007/BF01173936

    Article  Google Scholar 

  8. Chandrasekharaiah DS (1986) Thermoelasticity with second sound—a review. Appl Mech Rev 39:355–376. https://doi.org/10.1115/1.3143705

    Article  MATH  Google Scholar 

  9. Tang YX, Xu K (1995) Dynamic analysis of a piezothermoelastic laminated plate. J Therm Stresses 18:87–104. https://doi.org/10.1080/01495739508946292

  10. Yang JS, Batra RC (1995) Free vibrations of a linear thermo-piezoelectric body. J Therm Stresses 18:247–262. https://doi.org/10.1080/01495739508946301

  11. Moghadam PY, Tahani M, Naserian-Nik AM (2003) Analytical solution of piezolaminated rectangular plates with arbitrary clamped/simply-supported boundary conditions under thermo-electro-mechanical loadings. Appl Math Modell 37(5):3228–3241. https://doi.org/10.1016/j.apm.2012.07.034

  12. Sabzikar Boroujerdy M, Eslami MR (2014) Axisymmetric snap-through behavior of Piezo-FGM shallow clamped spherical shells under thermo-electro-mechanical loading. Int J Press Vessels Pip 120:19–26. https://doi.org/10.1016/j.ijpvp.2014.03.008

    Article  Google Scholar 

  13. Ponnusamy P, Selvamani R (2013) Wave propagation in magneto thermo elastic cylindrical panel. European J Mech A Solids 39:76–85. https://doi.org/10.1016/j.euromechsol.2012.11.004

  14. Selvamani R (2017) Stress waves in a generalized thermos elastic polygonal plate of inner and outer cross sections. J Solid Mech 9(2):263–275

    Google Scholar 

  15. Selvamani R, Mahinde OD (2018) Influence of rotation on transversely isotropic piezo electric rod coated with thin film. Eng Trans 66(3):211–220

    Google Scholar 

  16. De SN, Sengupta PR (1972) Magneto-elastic waves and disturbances in initially stressed conducting media. Pure Appl Geophys 93:41–54. https://doi.org/10.1007/bf00875220

  17. Acharya DP, Sengupta PR (1978) Magneto-thermo-elastic waves in an initially stressed conducting layer. Gerlands Beitr Geophys 87:229–239. https://doi.org/10.1007/BF02745739

    Article  Google Scholar 

  18. Acharya DP, Sengupta PR (1978) Magneto-thermo-elastic surface waves in initially stressed conducting media. Acta Geophys Polonica 26:299–311

    Google Scholar 

  19. Gubbins D (1990) Seismology and plate tectonics. Cambridge University Press, Cambridge

    Google Scholar 

  20. Kundu S, Pandit DK, Gupta S, Manna S (2016) Love wave propagation in a fiber-reinforced medium sandwiched between an isotropic layer and gravitating half-space. J Eng Math 100(1):109–119. https://doi.org/10.1002/nag.2254

    Article  MathSciNet  MATH  Google Scholar 

  21. Vinh PC, Anh VTN (2014) Rayleigh waves in an orthotropic half-space coated by a thin orthotropic layer with sliding contact. Int J Eng Sci 75:154–164(2014)

    Google Scholar 

  22. Paul HS, Renganathan K (1985) Free vibration of a pyroelectric layer of hexagonal (6 mm) class. J Acoust Soc America 78(2):395–397. https://doi.org/10.1007/BF01177170

    Article  Google Scholar 

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Selvamani, R., Panneer Selvam, R. (2021). Effect of Hydrostatic Stress and Piezoelasticity in a Thermopiezoelectric Layer Resting on Gravitating Half Space with Slip Interface. In: Rushi Kumar, B., Sivaraj, R., Prakash, J. (eds) Advances in Fluid Dynamics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-4308-1_47

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  • DOI: https://doi.org/10.1007/978-981-15-4308-1_47

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-4307-4

  • Online ISBN: 978-981-15-4308-1

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