Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Rayleigh wave at imperfectly corrugated interface in FGPM structure

  • K. Hemalatha (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology) ;
  • S. Kumar (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology) ;
  • A. Akshaya (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology)
  • Received : 2023.03.16
  • Accepted : 2023.08.21
  • Published : 2023.08.25
⟨ Previous Next ⟩

Abstract

The Rayleigh wave propagation is considered in the structure of the functionally graded piezoelectric material (FGPM) layer over the elastic substrate. The elastic substrate loosely bonds the layer through a corrugated interface, whereas its upper boundary is also corrugated but stress-free. Additionally, the solutions for the FGPM layer and substrate are derived using the fundamental variable separable approach to convert the partial differential equation to an ordinary differential equation. The results with boundary conditions lead to dispersion relations for the electrically open and electrically short cases in the determinant form. The outcomes have been numerically analyzed using a specific model. The findings were presented in the form of graphs, which were created using Mathematica 7. Graphs are plotted for variations in wavenumber and phase velocity. The outcomes may help measure interface defects and design Surface Acoustic Wave (SAW) devices.

Keywords

Acknowledgement

One of the authors express their sincere thanks to SRM Institute of Science and Technology, Kattankulathur, India, for providing the research fellowship and necessary research facility. Authors are also thankful to the reviewers for their valuable comments and suggestions to improve the quality of the paper.

References

  1. Abubakar, I. (1962), "Reflection and refraction of plane SH waves at irregular interfaces. II", J. Phys. Earth, 10(1), 15-20. https://doi.org/10.4294/jpe1952.10.15
  2. Abubakar, I. (1962), "Scattering of plane elastic waves at rough surfaces. I", Math. Proc. Cambridge Philos. Soc., 58(1),136-157. https://doi.org/10.1017/S030500410003629X
  3. Asano, S. (1960), "Reflection and refraction of elastic waves at a corrugated boundary surface. Part I. The case of incidence of SH wave", Bull. Earthq. Res. Inst., Univ. Tokyo, 38(2), 177-197.
  4. Asano, S. (1961), "Reflection and refraction of elastic waves at a corrugated boundary surface, II", Bull. Earthq. Res. Inst., Univ. Tokyo, 39, 367-406.
  5. Asano, S. (1966), "Reflection and refraction of elastic waves at a corrugated interface", Bull. Seismol. Soc. Am., 56(1), 201-221. https://doi.org/10.1785/BSSA0560010201.
  6. Belyankova, T.I., Vorovich, E.I., Kalinchuk, V.V. and Tukodova, O.M. (2021), "Features of Rayleigh waves propagation in structures with FGPM coating made of various materials", Physics and Mechanics of New Materials and Their Applications: Proceedings of the International Conference PHENMA 2020, 245-259.
  7. Bubakar, I. (1962), "Reflection and Refraction of plane SH Waves at Irregular Interfaces I", J. Phys. Earth, 10(1), 1-14. https://doi.org/10.4294/jpe1952.10.1
  8. Cao, X., Jin, F., Jeon, I. and Lu, T.J. (2009), "Propagation of Love waves in a functionally graded piezoelectric material (FGPM) layered composite system", Int. J. Solid. Struct., 46(22-23), 4123-4132. https://doi.org/10.1016/j.ijsolstr.2009.08.005.
  9. Chaki, M.S. and Singh, A.K. (2020), "The impact of reinforcement and piezoelectricity on SH wave propagation in irregular imperfectly-bonded layered FGPM structures: An analytical approach", Eur. J. Mech.-A/Solid., 80, 103872. https://doi.org/10.1016/j.euromechsol.2019.103872.
  10. Du, J., Jin, X., Wang, J. and Xian, K. (2007), "Love wave propagation in functionally graded piezoelectric material layer", Ultrasonic., 46(1), 13-22. https://doi.org/10.1016/j.ultras.2006.09.004.
  11. Dunkin, J.W. and Eringen, A.C. (1962), "The reflection of elastic waves from a free or fixed, wavy boundary of a half-space", Proceedings of the 4th U.S. National Congress on Applied Mechanics, Berkeley, 143-160.
  12. Guo, F.L. and Sun, R. (2008), "Propagation of Bleustein-Gulyaev wave in 6 mm piezoelectric materials loaded with viscous liquid", Int. J. Solid. Struct., 45(13), 3699-3710. https://doi.org/10.1016/j.ijsolstr.2007.09.018.
  13. Gupta, S. (1987), "Reflection and transmission of SH-waves in laterally and vertically heterogeneous media at an irregular boundary", Geophys. Transac., 33(2), 89-111.
  14. Hemalatha, K., Kumar, S. and Prakash, D. (2023), "Dispersion of Rayleigh wave in a functionally graded piezoelectric layer over elastic substrate", Forc. Mech., 10, 100171. https://doi.org/10.1016/j.finmec.2023.10017.
  15. Hua, L.I.U., Yang, J.L. and Liu, K.X. (2007), "Love waves in layered graded composite structures with imperfectly bonded interface", Chin. J. Aeronaut., 20(3), 210-214. https://doi.org/10.1016/S1000-9361(07)60034-X.
  16. Jakoby, B. and Vellekoop, M.J. (1997), "Properties of Love waves: Applications in sensors", Smart Mater. Struct., 6(6), 668.
  17. Jin, F., Qian, Z., Wang, Z. and Kishimoto, K. (2005), "Propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress", Smart Mater. Struct., 14(4), 515. https://doi.org/10.1088/0964-1726/14/4/009.
  18. Jones, J.P. and Whittier, J.S. (1967), "Waves at a flexibly bonded interface", Appl. Mech., 34(4), 905-909. https://doi.org/10.1115/1.3607854.
  19. Kaur, J., Tomar, S.K. and Kaushik, V.P. (2005), "Reflection and refraction of SH-waves at a corrugated interface between two laterally and vertically heterogeneous viscoelastic solid half-spaces", Int. J. Solid. Struct., 42(13), 3621-43. https://doi.org/10.1016/j.ijsolstr.2004.11.014.
  20. Kumar, R., Tomar, S.K. and Chopra, A. (2003), "Reflection/refraction of SH-waves at a corrugated interface between two different anisotropic and vertically heterogeneous elastic solid half-spaces", ANZIAM J., 44(3), 447-460. https://doi.org/10.1017/S1446181100008130.
  21. Kundu, S., Manna, S. and Gupta, S. (2014), "Love wave dispersion in pre-stressed homogeneous medium over a porous half-space with irregular boundary surfaces", Int. J. Solid. Struct., 51(21-22), 3689-3697. https://doi.org/10.1016/j.ijsolstr.2014.07.002.
  22. Lavrentyev, A.I. and Rokhlin, S.I. (1998), "Ultrasonic spectroscopy of imperfect contact interfaces between a layer and two solids", J. Acoust. Soc. Am., 103(2), 657-664. https://doi.org/10.1121/1.423235.
  23. Li, K., Jing, S., Yu, J. and Zhang, B. (2021), "Complex Rayleigh waves in nonhomogeneous magneto-electro-elastic half-spaces", Mater., 14(4), 1011. https://doi.org/10.3390/ma14041011.
  24. Li, X.Y., Wang, Z.K. and Huang, S.H. (2004), "Love waves in functionally graded piezoelectric materials", Int. J. Solid. Struct., 41(26), 7309-7328. https://doi.org/10.1016/j.ijsolstr.2004.05.064.
  25. Liang, Y., Li, Y., Liu, Y., Han, Q. and Liu, D. (2019), "Investigation of wave propagation in piezoelectric helical waveguides with the spectral finite element method", Compos. Part B: Eng., 160, 205- 216. https://doi.org/10.1016/j.compositesb.2018.09.083.
  26. Liu, C., Yu, J., Zhang, B., Zhang, X. and Elmaimouni, L. (2021), "Analysis of Lamb wave propagation in a functionally graded piezoelectric small-scale plate based on the modified couple stress theory", Compos. Struct., 265, 113733. https://doi.org/10.1016/j.compstruct.2021.113733.
  27. Liu, G.R., Han, X. and Lam, K.Y. (1999), "Stress waves in functionally gradient materials and its use for material characterization", Compos. Part B: Eng., 30(4), 383-394. https://doi.org/10.1016/S1359-8368(99)00010-4.
  28. Liu, Y., Lin, S., Li, Y., Li, C. and Liang, Y. (2019), "Numerical investigation of Rayleigh waves in layered composite piezoelectric structures using the SIGA-PML approach", Compos. Part B: Eng., 158, 230-238. https://doi.org/10.1016/j.compositesb.2018.09.037.
  29. Murty, G. (1975), "A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely bonded interface of elastic half spaces", Phys. Earth Planet. Interior., 11(1), 65-79. https://doi.org/10.1016/0031-9201(75)90076-X.
  30. Pal, P.C., Kumar, S. and Bose, S. (2015), "Propagation of Rayleigh waves in anisotropic layer overlying a semi-infinite sandy medium", Ain Shams Eng. J., 6(2), 621-627. https://doi.org/10.1016/j.asej.2014.11.003. 
  31. Qian, Z., Jin, F., Wang, Z. and Kishimoto, K. (2004), "Love waves propagation in a piezoelectric layered structure with initial stresses", Acta Mechanica, 171, 41-57. https://doi.org/10.1007/s00707-004-0128- 8.
  32. Ray, A. and Singh, A.K. (2021), "Impact of imperfect corrugated interface in piezoelectric-piezomagnetic composites on reflection and refraction of plane waves", J. Acoust. Soc. Am., 150(1), 573-591. https://doi.org/10.1121/10.0005544.
  33. Saha, S., Singh, A.K. and Chattopadhyay, A. (2021), "Impact of curved boundary on the propagation characteristics of Rayleigh-type wave and SH-wave in a prestressed monoclinic media", Mech. Adv. Mater. Struct., 28(12), 1274-1287. https://doi.org/10.1080/15376494.2019.1660930.
  34. Singh, A.K., Kumar, S. and Chattopadhyay, A. (2014), "Effect of irregularity and heterogeneity on the stresses produced due to a normal moving load on a rough monoclinic half-space", Meccanica, 49, 2861-2878. https://doi.org/10.1007/s11012-014-0033-8.
  35. Singh, S.S. (2011), "Love wave at a layer medium bounded by irregular boundary surfaces", J. Vib. Control, 17(5), 789-795. https://doi.org/10.1177/10775463093513.
  36. Singh, S.S. (2011), "Response of shear wave from a corrugated interface between elastic solid/viscoelastic half-spaces", Int. J. Numer. Anal. Meth. Geomech., 35(5), 529- 543. https://doi.org/10.1002/nag.901.
  37. Singh, S.S. and Tomar, S.K. (2008), "qP-wave at a corrugated interface between two dissimilar pre-stressed elastic half-spaces", J. Sound Vib., 317(3-5), 687-708. https://doi.org/10.1016/j.jsv.2008.03.036.
  38. Singhal, A., Sahu, S.A. and Chaudhary, S. (2018), "Approximation of surface wave frequency in piezocomposite structure", Compos. Part B: Eng., 144, 19-28. https://doi.org/10.1016/j.compositesb.2018.01.017.
  39. Slavin, L.M. and Wolf, B. (1970), "Scattering of Love waves in a surface layer with an irregular boundary for the case of a rigid underlying half-space", Bull. Seismol. Soc. Am., 60(3), 859-877. https://doi.org/10.1785/BSSA0600030859.
  40. Sumner, J.H. and Deresiewicz, H. (1972), "Waves in an elastic plate with an irregular boundary", Pure Appl. Geophys., 96, 106-126. https://doi.org/10.1007/BF00875633.
  41. Tomar, S., Kumar, R. and Chopra, A. (2002), "Reflection/refraction of SH waves at a corrugated interface between transversely isotropic and visco-elastic solid half-spaces", Acta Geophysica Polonica, 50(2), 231-249.
  42. Tomar, S.K. and Kaur, J. (2003), "Reflection and transmission of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic solid half-spaces", Earth Planet. Space, 55(9), 531-547. https://doi.org/10.1186/BF03351786
  43. Tomar, S.K. and Kaur, J. (2007), "SH-waves at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space", Acta Mechanica, 190(1-4), 1-28. https://doi.org/10.1007/s00707-006-0423-7.
  44. Tomar, S.K. and Saini, S.L. (1997), "Reflection and refraction of SH-waves at a corrugated interface between two-dimensional transversely isotropic half-spaces", J. Phys. Earth, 45(5), 347-62. https://doi.org/10.4294/jpe1952.45.347
  45. Tomar, S.K. and Sarat Singh, S. (2006), "Plane SH-waves at a corrugated interface between two dissimilar perfectly conducting self-reinforced elastic half-spaces", Int. J. Numer. Anal. Meth. Geomech., 30(6), 455-487. https://doi.org/10.1002/nag.485.
  46. Wu, T.T. and Wu, T.Y. (2000), "Surface waves in coated anisotropic medium loaded with viscous liquid", J. Appl. Mech., 67(2), 262-266. https://doi.org/10.1115/1.1304840.
  47. Zhang, R. and Shinozuka, M. (1996), "Effects of irregular boundaries in a layered half-space on seismic waves", J. Sound Vib., 195(1), 1-16. https://doi.org/10.1006/jsvi.1996.0400.