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Rayleigh Waves in an Electroelastic Medium with Prestressed Inhomogeneous Coating

  • ON THE ANNIVERSARY OF ALEXANDER KONSTANTINOVICH BELYAEV
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Abstract

An approach to studying the influence of initial mechanical stresses and an electrostatic field on the structure and behavior of Rayleigh waves in piezoelectric media with nonhomogeneous coatings is proposed. This paper considers two-component coatings made of functionally graded piezoelectric material with high-speed (the speed of the shear-wave inclusion is greater than the speed of the shear wave in the substrate) or low-speed (the speed of the shear-wave inclusion is less than the speed of the shear wave in the substrate) inclusions. The initially deformed state of the coating is induced by the separate or combined action of the initial mechanical stresses and external electrostatic field. The influence of the type of non-homogeneity and the nature of the initial mechanical stresses in the presence or absence of an initial electrostatic field on the features of Rayleigh wave propagation for problems with an electrically open or shorted surface is studied. It is established that the presence of a low-intensity initial electrostatic field only slightly affects the action of the initial mechanical stresses depending on its direction. The presence of a high-intensity electrostatic field leads to additional deformation of the material, significant changes in the speeds of the SAW modes, and substantial changes in the structure of the surface-wave field. The obtained results are presented in dimensionless parameters and may be of practical interest in the development, design, and optimization of new materials for micro- and nanoscale devices and devices on Rayleigh surface acoustic waves with high performance characteristics.

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REFERENCES

  1. W. P. Mason, Physical Acoustics and the Properties of Solids (Van Nostrand, Princeton, N.J., 1958).

    Google Scholar 

  2. I. A. Viktorov, Rayleigh and Lamb Waves: Physical Theory and Applications (Nauka, Moscow, 1966; Plenum, New York, 1967).

  3. E. Dieulesaint and D. Royer, Ondes Elastiques Dans Les Solides. Application au Traitement du Signal (Ed. Masson, Paris, 1974).

  4. Surface Wave Filters. Design, Construction and Use, Ed. by H. Matthews (Wiley, New York, 1977).

    Google Scholar 

  5. J. D. Achenbach, Wave Propagation in Elastic Solids (North-Holland, Amsterdam, 1973).

    Google Scholar 

  6. B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, Malabar, Fla., 1990), Vol. 2.

    Google Scholar 

  7. S. V. Biryukov, Y. V. Gulyaev, V. V. Krylov, and V. P. Plessky, Surface Acoustic Waves in Inhomogeneous Media (Springer-Verlag, New York, 1995).

    Book  Google Scholar 

  8. A. L. Shuvalov and A. G. Every, “Some properties of surface acoustic waves in anisotropic-coated solids, studied by the impedance method,” Wave Motion 36, 257–273 (2002). https://doi.org/10.1016/S0165-2125(02)00013-6

    Article  MathSciNet  Google Scholar 

  9. R. V. Gol’dshtein and S. V. Kuznetsov, “Surface acoustic waves in the testing of layered media. The waves’ sensitivity to variations in the properties of the individual layers,” J. Appl Math. Mech. 77, 51–56 (2013).https://doi.org/10.1016/j.jappmathmech.2013.04.007

    Article  Google Scholar 

  10. T. I. Belyankova and V. V. Kalinchuk, “On the problem of analyzing the dynamic properties of a layered half-space,” Acoust. Phys. 60, 530–542 (2014). https://doi.org/10.1134/S1063771014050017

    Article  Google Scholar 

  11. V. I. Alshits and G. A. Maugin, “Dynamics of multilayers: Elastic waves in an anisotropic graded or stratified plate,” Wave Motion 41, 357–394 (2005). https://doi.org/10.1016/j.wavemoti.2004.09.002

    Article  MathSciNet  Google Scholar 

  12. M. Destrade, “Seismic Rayleigh waves on an exponentially graded, orthotropic halfspace,” in Proc.: Math., Phys. Eng. Sci. 463, 495–502 (2007). http://www.jstor.org/stable/20209130.

  13. V. V. Kalinchuk and T. I. Belyankova, Dynamic Contact Problems for Prestressed Bodies (Fizmatlit, Moscow, 2002) [in Russian].

    Google Scholar 

  14. B. A. Auld, “Wave propagation and resonance in piezoelectric materials,” J. Acoust. Soc. Am. 70, 1577–1585 (1981). https://doi.org/10.1121/1.387223

    Article  Google Scholar 

  15. L. P. Zinchuk and A. N. Podlipenets, “Dispersion equations for Rayleigh waves in a piezoelectric periodically layered structure,” J. Math. Sci. 103, 398–403 (2001). https://doi.org/10.1023/A:1011382816558

    Article  MathSciNet  Google Scholar 

  16. C. Othmani, L. Labiadh, C. Lu, A. R. Kamali, and F. Takali, “Influence of a piezoelectric ZnO intermediate layer on Rayleigh waves propagating in Sc43%AlN57%/ZnO/diamond hetero-structures subjected to uniaxial stress,” Eur. Phys. J. Plus 135, 898 (2020). https://doi.org/10.1140/epjp/s13360-020-00912-9

    Article  Google Scholar 

  17. V. A. Zhelnorovich, “Rayleigh and Bleustein–Gulyayev surface waves in elastic piezoelectric materials with relaxation of dielectric polarization,” J. Appl. Math. Mech. 79, 186–194 (2015). https://doi.org/10.1016/j.jappmathmech.2015.07.010

  18. N. Favretto-Cristini, D. Komatitsch, J. M. Carcione, and F. Cavallini, “Elastic surface waves in crystals. Part 1: Review of the physics,” Ultrasonics 51, 653–660 (2011). https://doi.org/10.1016/j.ultras.2011.02.007

    Article  Google Scholar 

  19. W. Wang, J. Liang, Y. Ruan, W. Pang, and Z. You, “Design and fabrication of an surface acoustic wave resonator based on AlN/4H-SiC material for harsh environments,” J. Zhejiang Univ.-SCIENCE A 18, 67–74 (2017). https://doi.org/10.1631/jzus.a1600028

    Article  Google Scholar 

  20. H. F. Tiersten, “Elecrtoelastic interactions and the piezoelectric equations,” J. Acoust. Soc. Am. 70, 1567–1576 (1981).

    Article  Google Scholar 

  21. V. V. Kalinchuk and T. I. Belyankova, Dynamic Contact Problems for Prestressed Electroelastic Bodies (Fizmatlit, Moscow, 2006) [in Russian].

    Google Scholar 

  22. O. V. Evdokimova, T. I. Belyankova, and V. V. Kalinchuk, “Equations of dynamics of prestressed piezoactive medium in the presence of external electrostatic field,” Vestn. Yuzhn. Nauchn. Tsentra Ross. Akad. Nauk 3 (4), 19–25 (2007).

    Article  Google Scholar 

  23. T. I. Belyankova, V. V. Kalinchuk, and D. N. Sheidakov, “Dynamics equations for prestressed electrothermoelastic medium,” Vestn. Yuzhn. Nauchn. Tsentra Ross. Akad. Nauk 7 (2), 5–14 (2011).

    Google Scholar 

  24. S. I. Burkov, O. P. Zolotova, and B. P. Sorokin, “Influence of bias electric field on elastic waves propagation in piezoelectric layered structures,” Ultrasonics 53, 1059–1064 (2013).

    Article  Google Scholar 

  25. X. Cao, F. Jin, and Z. Wang, “On dispersion relations of Rayleigh waves in a functionally graded piezoelectric material (FGPM) half-space,” Acta Mech. 200, 247–261 (2008). https://doi.org/10.1007/s00707-008-0002-1

    Article  Google Scholar 

  26. I. Ben Salah, A. Njeh, and M. H. Ben Ghozlen, “A theoretical study of the propagation of Rayleigh waves in a functionally graded piezoelectric material (FGPM),” Ultrasonics 52, 306–314 (2012). https://doi.org/10.1016/j.ultras.2011.08.016

    Article  Google Scholar 

  27. K. Hemalatha, S. Kumar, and D. Prakash, “Dispersion of Rayleigh wave in a functionally graded piezoelectric layer over elastic substrate,” Forces Mech. 10, 100171 (2023). https://doi.org/10.1016/j.finmec.2023.100171

    Article  Google Scholar 

  28. H. Ezzin, M. Mkaoir, and M. B. Amor, “Rayleigh wave behavior in functionally graded magnetoelectro-elastic material,” Superlattices Microstruct. 112, 455–469 (2017). doi 10.1016 /j.spmi.2017.10.001

  29. T. I. Belyankova, E. I. Vorovich, V. V. Kalinchuk, and O. M. Tukodova, “Features of Rayleigh waves propagation in structures with FGPM coating made of various materials,” in Physics and Mechanics of New Materials and Their Applications (Springer-Verlag, Cham, 2021), in Ser.: Springer Proceedings in Materials, Vol. 10, pp. 245–259. https://doi.org/10.1007/978-3-030-76481-4_22

  30. T. I. Belyankova and V. V. Kalinchuk, “On the dynamics of an inhomogeneous prestressed electroelastic medium under the influence of an external electric field,” Mech. Solids 56, 242–250 (2021). https://doi.org/10.3103/S0025654421070098

    Article  Google Scholar 

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Funding

The research was carried out within the framework of the implementation of the state assignment of the Southern Scientific Center of the Russian Academy of Sciences (state registration no. 122020100343-4).

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Correspondence to T. I. Belyankova or V. V. Kalinchuk.

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Translated by K. Gumerov

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Belyankova, T.I., Kalinchuk, V.V. Rayleigh Waves in an Electroelastic Medium with Prestressed Inhomogeneous Coating. Vestnik St.Petersb. Univ.Math. 56, 424–434 (2023). https://doi.org/10.1134/S1063454123040040

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