Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A comprehensive analysis of horizontally polarized shear waves in a thin microstructural plate

  • Vikas Sharma (Department of Mathematics, Lovely Professional University) ;
  • Satish Kumar (School of Mathematics, Thapar Institute of Engineering and Technology)
  • Received : 2022.07.02
  • Accepted : 2023.01.26
  • Published : 2023.02.25
⟨ Previous Next ⟩

Abstract

Horizontally polarized shear waves (SH) have numerous applications in various scientific, engineering, and medical fields. The study deals with an investigation of SH-waves in a thin microstructural plate. The plate has been mathematically modelled by employing size dependent consistent couple stress theory, which involves a length parameter, known as characteristic length. Characteristic length is assumed to be of the order of internal microstructures of the material. Dispersion relations have been calculated for the propagation of SH-waves using different set of boundary conditions. Group velocity of the SH-waves has been calculated by using an analytical approach. The mathematical results obtained in the problem are discussed in detail and the impacts of characteristic length parameter and thickness of plate are presented on phase velocity of SH-waves through graphical illustrations.

Keywords

References

  1. Ahmetolan, S. and Demirci, A. (2014), "Interaction of nonlinear SH waves in a two layered elastic plate", ICSV21, Beijing, China, July.
  2. Alshits, V.I., Deschamps, M. and Lyubimov, V.N. (2005), "Dispersion anomalies of shear horizontal guided waves in two- and three-layered plates", J. Acoust. Soc. Am., 118, 2850-2859. https://doi.org/10.1121/1.2046807.
  3. Auld, B.A., Chimenti, D.E. and Shull, P.J. (1996), "Shear horizontal wave propagation in periodically layered composites," IEEE Tran. Ultrason., Ferroelec. Frequen. Control, 43(2), 319-325. https://doi.org/10.1109/58.485959.
  4. Castaings, M. and Hosten, B. (2001), "Lamb and SH waves generated and detected by air-coupled ultrasonic transducers in composite material plates", NDT E Int., 34(4), 249-258. https://doi.org/10.1016/S0963-8695(00)00065-7.
  5. Chaudhary, S., Kaushik, V.P. and Tomar, S.K. (2005), "Transmission of shear waves through a self-reinforced layer sandwiched between two inhomogeneous viscoelastic half-spaces", Int. J. Mech. Sci., 47(9), 1455-1472. https://doi.org/10.1016/j.ijmecsci.2005.04.011.
  6. Chimenti, D.E. (1997), "Guided waves in plates and their use in materials characterization", Appl. Mech. Rev., 50(5), 247-284. https://doi.org/10.1115/1.3101707.
  7. Djeran-Maigre, I. and Kuznetsov, S.V. (2014), "Velocities, dispersion, and energy of SH-waves in anisotropic laminated plates", Acoust. Phys., 60, 200-207. https://doi.org/10.1134/S106377101402002X.
  8. Fakhrabadi, M.M.S. (2015), "Size effects on nanomechanical behaviors of nanoelectronics devices based on consistent couple-stress theory", Int. J. Mech. Sci., 92, 146-153. https://doi.org/10.1016/j.ijmecsci.2014.12.009.
  9. Fan, H. and Xu, L. (2018), "Love wave in a classical linear elastic half-space covered by a surface layer described by the couple stress theory", Acta Mechanica, 229, 5121-5132. https://doi.org/10.1007/s00707-018-2293-1.
  10. Gitis, A. and Sauer, D.U. (2016), "The propagation of horizontally polarized shear waves in plates bordered with viscous liquid", Ultrasonic., 71, 264-270. https://doi.org/10.1016/j.ultras.2016.06shar.018.
  11. Graff, K.F. (1975), Wave Motion in Elastic Solids, Dover Publications, New York, USA.
  12. Hadjesfandiari, A.R. and Dargush, G.F. (2011), "Couple stress theory for solids", Int. J. Solid. Struct., 48(18), 2496-2510. https://doi.org/10.1016/j.ijsolstr.2011.05.002.
  13. Ilyashenko, A. and Kuznetsov, S. (2018), "SH waves in anisotropic (monoclinic) media", J. Appl. Math. Phys., 69, 17. https://doi.org/10.1007/s00033-018-0916-y.
  14. Jiangong, Y. (2011), "Viscoelastic shear horizontal wave in graded and layered plates", Int. J. Solid. Struct., 48(16-17), 2361-2372. https://doi.org/10.1016/j.ijsolstr.2011.04.011.
  15. Josse, F., Bender, F. and Cernosek, R.W. (2001), "Guided shear horizontal surface acoustic wave sensors for chemical and biochemical detection in liquids", Anal. Chem., 73(24), 5937-5944. https://doi.org/10.1021/ac010859e.
  16. Kimura, T., Omura, M., Kishimoto, Y. and Hashimoto, K. (2019), "Comparative study of acoustic wave devices using thin piezoelectric plates in the 3-5-ghz range", IEEE Tran. Microw. Theor. Techniq., 67(3), 915-921. https://doi.org/10.1109/TMTT.2018.2890661.
  17. Kuznetsov, S.V. (2006), "SH-waves in laminated plates", Quart. Appl. Math., 64, 153-165. https://doi.org/10.1090/S0033-569X-06-00992-1.
  18. Miao, H. and Li, F. (2021), "Shear horizontal wave transducers for structural health monitoring and nondestructive testing: A review", Ultrasonic., 114, 106355. https://doi.org/10.1016/j.ultras.2021.106355.
  19. Nejad, M.Z., Hadi, A. and Farajpour, A. (2017), "Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials", Struct. Eng. Mech., 63(2), 161-169. https://doi.org/10.12989/sem.2017.63.2.161.
  20. Nobili, A. (2021), "Asymptotically consistent size-dependent plate models based on the couple-stress theory with micro-inertia", Eur. J. Mech.-A/Solid., 89, 104316. https://doi.org/10.1016/j.euromechsol.2021.104316.
  21. Pandit, D.K., Kundu, S. and Gupta, S. (2017), "Analysis of dispersion and absorption characteristics of shear waves in sinusoidally corrugated elastic medium with void pores", Roy. Soc. Open Sci., 4, 160511. https://doi.org/10.1098/rsos.160511.
  22. Saitoh, T. and Ishiguro, A. (2021), "Surface crack detection in a thin plate using time reversal analysis of SH guided waves", Struct. Eng. Mech., 80(3), 243-251. https://doi.org/10.12989/sem.2021.80.3.243.
  23. Sharma, V. and Kumar, S. (2016), "Influence of microstructure, heterogeneity and internal friction on SH waves propagation in a viscoelastic layer overlying a couple stress substrate", Struct. Eng. Mech., 57(4), 703-716. https://doi.org/10.12989/sem.2016.57.4.703.
  24. Sharma, V. and Kumar, S. (2018), "Dispersion of rayleigh waves in a microstructural couple stress substrate loaded with liquid layer under the effects of gravity", Arch. Acoust., 43(1), 11-20. https://doi.org/10.24425/118076.
  25. Sharma, V., Goyal, R. and Kumar, S. (2020), "Love waves in a layer with void pores over a microstructural couple stress substrate with corrugated boundary surfaces", J. Brazil. Soc. Mech. Sci. Eng., 42, 1-16. https://doi.org/10.1007/s40430-020-2262-1.
  26. Simonetti, F. and Cawley, P. (2004), "On the nature of shear horizontal wave propagation in elastic plates coated with viscoelastic materials", Proc. Roy. Soc. London-A, 460(2048), 2197-2221. https://doi.org/10.1098/rspa.2004.1284.
  27. Simonova, K., Honzik, P., Bruneau, M. and Gatignol, P. (2020), "Modelling approach for MEMS transducers with rectangular clamped plate loaded by a thin fluid layer", J. Sound Vib., 473, 115246. https://doi.org/10.1016/j.jsv.2020.115246.
  28. Singh, A.K., Agarwalla, S., Chaki, M.S. and Chattopadhyay, A. (2021), "Shear wave propagation in a slightly compressible finitely deformed layer over a foundation with pre-stressed fibre-reinforced stratum and dry sandy viscoelastic substrate", Wave. Random Complex Media, 31(5), 847-866. https://doi.org/10.1080/17455030.2019.1631503.
  29. Singh, A.K., Ray, A. and Chattopadhyay, A. (2019), "Analytical study on propagation of g-type waves in a transversely isotropic substrate beneath a stratum considering couple stress", Int. J. Geomech., 19(7), 04019071. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001454.
  30. Sun, K., Feng, H.C.Q. and Lei, X. (2020), "Propagation characteristics of ultrasonic guided waves in tram rails", Struct. Eng. Mech., 75(4), 435-444. https://doi.org/10.12989/sem.2020.75.4.435.
  31. Vardoulakis, I. and Georgiadis, H.G. (1997), "SH surface waves in a homogeneous gradient-elastic half-space with surface energy", J. Elast., 47, 147-165. https://doi.org/10.1023/A:1007433510623.
  32. Vavva, M.G., Protopappas, V.C., Gergidis, L.N., Charalambopoulos, A., Fotiadis, D.I. and Polyzos D. (2009), "Velocity dispersion of guided waves propagating in a free gradient elastic plate: Application to cortical bone", J. Acoust. Soc. Am., 125(5), 3414-27. https://doi.org/10.1121/1.3110203.
  33. Yang, P.S., Liu, S.W. and Sung, J.C. (2008), "Transient response of SH waves in a layered half-space with sub-surface and interface cracks", Appl. Math. Model., 32, 595-609. https://doi.org/10.1016/j.apm.2007.01.006.
  34. Zagrouba, M. and Bouhdima, M.S. (2021), "Investigation of SH wave propagation in piezoelectric plates", Acta Mechanica, 232, 3363-3379. https://doi.org/10.1007/s00707-021-02990-x.
  35. Zakharenko, A.A. (2013), "Fundamental modes of new dispersive SH-waves in piezoelectromagnetic plate", Pramana-J. Phys., 81, 819-827. https://doi.org/10.1007/s12043-013-0609-1.