Reflection and Transmission of Plane Wave at an Interface Between Two Rotating Micropolar Piezoelectric Solid Half-Spaces
Abstract
In this paper, we investigate a problem on reflection and transmission of plane-waves at an interface between two dissimilar half-spaces of a transversely isotropic micropolar piezoelectric material. The entire model is assumed to rotate with a uniform angular velocity. The governing equations of rotating and transversely isotropic micropolar piezoelectric medium are specialized in a plane. Plane-wave solutions of two-dimensional coupled governing equations show the possible propagation of three coupled plane-waves. For an incident plane-wave at an interface between two dissimilar half-spaces, three reflected and three transmitted waves propagate with distinct speeds. The connections between the amplitude ratios of reflected and transmitted waves are obtained. The expressions for the energy ratios of reflected and transmitted waves are also obtained. A numerical example of the present model is considered to illustrate the effects of rotation on the speeds and energy ratios graphically.Keywords:
plane-wave, micropolar piezoelectricity, reflection and transmission, amplitude ratios, energy ratios, rotationReferences
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2. Alshits V.I., Lothe J., Lyubimov V.N. (1984), The phase shift for reflection of elastic waves in hexagonal piezoelectric crystals, Wave Motion, 6(3): 259–264, https://doi.org/10.1016/0165-2125%2884%2990029-5
3. Alshits V.I., Shuvalov A.L. (1995), Resonance reflection and transmission of shear elastic waves in multilayered piezoelectric structures, Journal of Applied Physics, 77(6): 2659–2665, https://doi.org/10.1063/1.358732
4. Aouadi M. (2008), Aspects of uniqueness in micropolar piezoelectric bodies, Mathematics and Mechanics of Solids, 13: 499–512, doi: 10.1177%2F1081286507077106.
5. Auld B.A. (1973), Acoustic Fields and Waves in Solids, Wiley Interscience, New York.
6. Auld B.A. (1981), Wave propagation and resonance in piezoelectric materials, The Journal of the Acoustical Society of America, 70(6): 1577–1585, https://doi.org/10.1121/1.387223
7. Barati M.R., Zenkour A.M. (2018), Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions, Journal of Vibration and Control, 24(10): 1910–1926, doi: 10.1177%2F1077546316672788.
8. Burkov S.I., Sorokin B.P., Aleksandrov K.S., Karpovich A.A. (2009), Reflection and refraction of bulk acoustic waves in piezoelectrics under uniaxial stress, Acoustical Physics, 55: 178–185, https://doi.org/10.1134/S1063771009020055
9. Cheng N.C., Sun C.T. (1975), Wave propagation in two-layered piezoelectric plates, The Journal of the Acoustical Society of America, 57(3): 632–638, https://doi.org/10.1121/1.380479
10. Ciumasu S.G., Vieru D. (1999), Variational formulations for the vibration of a micropolar piezoelectric body, The Journal of the Acoustical Society of America, 105(2): 1240, https://doi.org/10.1121/1.425960
11. Cracium I.A. (1995), Uniqueness theorem in the linear theory of piezoelectric micropolar thermoelasticity, International Journal of Engineering Science, 33: 1027–1036, https://doi.org/10.1016/0020-7225%2894%2900106-T
12. Darinskii A.N., Clezio E.L., Feuillard G. (2008), The role of electromagnetic waves in the reflection of acoustic waves in piezoelectric crystals, Wave Motion, 45(4): 428–444, https://doi.org/10.1016/j.wavemoti.2007.08.001
13. Ergin K. (1950), Energy ratio of the seismic waves reflected and refracted at a rock-water boundary, Bulletin of the Seismological Society of America, 42(4): 349–372, https://doi.org/10.1785/BSSA0420040349
14. Eringen A.C. (1966), Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics, 15(6): 909–923, https://www.jstor.org/stable/24901442
15. Eringen A.C. (1968), Theory of Micropolar Elasticity in Fracture, Vol. 2, Academic Press, pp. 621–729.
16. Eringen A.C. (1999), Microcontinuum Field Theories I: Foundations and Soilds, Springer, New York.
17. Every A.G., Neiman V.I. (1992), Reflection of electroacoustic waves in piezoelectric solids: Mode conversion into four bulk waves, Journal of Applied Physics, 71(12): 6018–6024, https://doi.org/10.1063/1.350457
18. Ewing W.M., Jardetzky W.S., Press F. (1957), Elastic Waves in Layered Media, McGraw-Hill Company Inc., New York, Toronto, London.
19. Gales C. (2012), Some results in micromorphic piezoelectricity, European Journal of Mechanics- A/Solids, 31(1): 37–46, https://doi.org/10.1016/j.euromechsol.2011.06.014
20. Guo X., Wei P. (2014), Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces, International Journal of Solids and Structures, 51(21–22): 3735–3751, https://doi.org/10.1016/j.ijsolstr.2014.07.008
21. Guo X., Wei P., Li L., Tang Q. (2015), Influences of mechanically and dielectrically imperfect interfaces on the reflection and transmission waves between two piezoelectric half spaces, International Journal of Solids and Structures, 63: 184–205, https://doi.org/10.1016/j.ijsolstr.2015.02.050
22. Gutenberg B. (1944), Energy ratio of reflected and refracted seismic waves, Bulletin of the Seismological Society of America, 34(2): 85–102, https://doi.org/10.1785/BSSA0340020085
23. Hruska K. (1966), The rate of propagation of ultrasonic waves in ADP in Voigt’s theory, Czechoslovak Journal of Physics B, 16(5): 446–454, https://doi.org/10.1007/BF01696256
24. Iesan D. (2006), On the microstretch piezoelectricity, International Journal of Engineering Science, 44(13–14): 819–829, https://doi.org/10.1016/j.ijengsci.2006.05.007
25. Jeffreys H. (1926), The reflexion and refraction of elastic waves, Geophysical Supplements to the Monthly Notices of the Royal Astronomical Society, 1(7): 321–334, https://doi.org/10.1111/j.1365-246X.1926.tb05380.x
26. Jiao F., Wei P., Zhou Y., Zhou X. (2019), Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces, European Journal of Mechanics-A/Solids, 75: 70–81, https://doi.org/10.1016/j.euromechsol.2019.01.007
27. Kaung Z.B. (2013), Theory of Electroelasticity, Springer.
28. Knott C.G. (1899), Reflexion and refraction of elastic waves with seismological applications, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 48: 64–97, https://doi.org/10.1080/14786449908621305
29. Kuang Z.B., Yuan X.G. (2011), Reflection and transmission of waves in pyroelectric and piezoelectric materials, Journal of Sound and Vibration, 330(6): 1111–1120, https://doi.org/10.1016/j.jsv.2010.09.026
30. Kyame J.J. (1949), Wave propagation in piezoelectric crystals, The Journal of the Acoustical Society of America, 21(3): 159–167, https://doi.org/10.1121/1.1906490
31. Liu C., Yu J., Wang X., Zhang B., Zhang X., Zhou H. (2021), Reflection and transmission of elastic waves through nonlocal piezoelectric plates sandwiched in two solid half-spaces, Thin-Walled Structures, 168: 108306, https://doi.org/10.1016/j.tws.2021.108306
32. Othman M.I.A., Elmaklizi Y.D., Ahmed E.A.A. (2017a), Effect of magnetic field on piezo-thermoelastic medium with three theories, Results in Physics, 7: 361–3368, https://doi.org/10.1016/j.rinp.2017.08.058
33. Othman M.I.A., Elmaklizi Y.D., Ahmed E.A.A. (2017b), Influence of magnetic field on generalized piezo-thermoelastic rotating medium with two relaxation times, Microsystem Technologies, 23, 5599–5612, https://doi.org/10.1007/s00542-017-3513-7
34. Pailloux P.M.H. (1958), Piezoelectricity. Calculation of propagation velocities [in French: Piézoélectricité. Calcul des vitesses de propagation], Le Journal De Physique Etle Radium, 19(5): 523–526, https://doi.org/10.1051/jphysrad%3A01958001905052300
35. Pal M.K., Singh A.K. (2021), Analysis of reflection and transmission phenomenon at distinct bonding interfaces in a rotating pre-stressed functionally graded piezoelectric-orthotropic structure, Applied Mathematics and Computation, 409: 126398, https://doi.org/10.1016/j.amc.2021.126398
36. Pang Y., Wang Y.S., Liu J.X, Fang D.N. (2008), Reflection and refraction of plane waves at the interface between piezoelectric and piezomagnetic media, International Journal of Engineering Science, 46(11): 1098–1110, https://doi.org/10.1016/j.ijengsci.2008.04.006
37. Parafitt V.R., Eringen A.C. (1969) Reflection of plane waves from the flat boundary of a micropolar elastic half-space, The Journal of the Acoustical Society of America, 45(5): 1258–1272, https://doi.org/10.1121/1.1911598
38. Parton V.Z., Kudryavtsev B.A. (1988), Electromagnetoelasticity: Piezoelectrics and Electrically Conductive Solids, Gordon and Beach, New York.
39. Rosenbaum J.F. (1988), Bulk Acoustic Wave Theory and Devices, Artech House, Boston.
40. Sahu S.A., Nirwal S., Mondal S. (2021), Reflection and transmission of quasi-plane waves at the interface of piezoelectric semiconductors with initial stresses, Applied Mathematics and Mechanics, 42(7): 951–968, https://doi.org/10.1007/s10483-021-2738-9
41. Sangwan A., Singh B., Singh J. (2018), Reflection and transmission of plane waves at an interface between elastic and micropolar piezoelectric solid half-spaces, Technische Mechanik, 38(3): 267–285, https://doi.org/10.24352/UB.OVGU-2018-034
42. Schoenberg M., Censor D. (1973), Elastic waves in rotating media, Quarterly of Applied Mathematics, 31(1): 115–125, https://doi.org/10.1090/qam/99708
43. Singh B. (2010), Wave propagation in a prestressed piezoelectric half-space, Acta Mechanica, 211(3): 337–344, https://doi.org/10.1007/s00707-009-0234-8
44. Singh B. (2013), Propagation of shear waves in a piezoelectric medium, Mechanics of Advanced Materials and Structures, 20(6): 434–440, https://doi.org/10.1080/15376494.2011.627633
45. Singh B., Sangwan A., Singh J. (2019), Reflection and transmission of elastic waves at an interface between two micropolar piezoelectric half-spaces, Journal of Ocean Engineering and Science, 4(3): 227–237, https://doi.org/10.1016/j.joes.2019.04.006
46. Singh B., Sindhu R. (2016), On propagation of Rayleigh type surface wave in a micropolar piezoelectric medium, Open Journal of Acoustics, 6(4): 35–44, https://doi.org/10.4236/oja.2016.64004
47. Singh B., Sindhu R. (2018), Rotational effects on propagation of Rayleigh wave in a micropolar piezoelectric medium, Journal of Theoretical and Applied Mechanics, Sofia, 48(2): 93–105, https://doi.org/10.2478/jtam-2018-0012
48. Singh S., Singh A.K., Guha S. (2021), Impact of interfacial imperfections on the reflection and transmission phenomenon of plane waves in a porous-piezoelectric model, Applied Mathematical Modelling, 100: 656–675, https://doi.org/10.1016/j.apm.2021.08.022
49. Tiersten H.F., Stevens D.S., Das P.K. (1980), Acoustic surface wave accelerometer and rotation rate sensor, [In:] Proceedings of IEEE Ultrasonics Symposium, pp. 692–695, https://doi.org/10.1109/ULTSYM.1980.197488
50. Tiersten H.F., Stevens D.S., Das P.K. (1981), Circulating flexural wave rotation rate sensor, [In:] Proceedings of IEEE Ultrasonics Symposium, pp. 163–166, https://doi.org/10.1109/ULTSYM.1981.197602
51. Vieru D., Ciumasu S.G. (1999), Love waves in nonclassical micropolar piezoelectricity, The Journal of the Acoustical Society of America, 105(2): 1241, https://doi.org/10.1121/1.426640
52. White R.W. (1998), Acoustic sensors for physical, chemical and biochemical applications, [In:] Proceedings of the 1998 IEEE International Frequency Control Symposium (Cat. No.98CH36165), pp. 587–594, https://doi.org/10.1109/FREQ.1998.717960
53. Wren T., Burdess J. S. (1987), Surface waves perturbed by rotation, ASME Journal of Applied Mechanics, 54(2): 464–466, https://doi.org/10.1115/1.3173043
54. Xue B. et al. (2012), Photo-induced effects in GeS2 glass and glass–ceramics stimulated by green and IR lasers, Materials Letters, 73: 14–16,doi: 10.1016%2Fj.matlet.2011.12.089.
55. Yuan X., Zhu Z.H. (2012), Reflection and refraction of plane waves at interface between two piezoelectric media, Acta Mechanica, 223(12): 2509–2521, https://doi.org/10.1007/s00707-012-0728-7
56. Zenkour A.M., Alghanmi R.A. (2019a), Bending of exponentially graded plates integrated with piezoelectric fiber-reinforced composite actuators resting on elastic foundations, European Journal of Mechanics-A/Solids, 75: 461–471, https://doi.org/10.1016/j.euromechsol.2019.03.003
57. Zenkour A.M., Alghanmi R.A. (2019b), Stress analysis of a functionally graded plate integrated with piezoelectric faces via a four-unknown shear deformation theory, Results in Physics, 12: 268–277, https://doi.org/10.1016/j.rinp.2018.11.045
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