Reflection and Transmission of Plane Wave at an Interface Between Two Rotating Micropolar Piezoelectric Solid Half-Spaces

• Autorzy: Singh Baljeet , Sangwan Asha , Singh Jagdish

Identyfikatory

DOI

10.24425/aoa.2021.138155

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

plane wave; micropolar piezoelectricity; reflection and transmission; amplitude ratios; energy ratios; rotation

• Wydawca: Instytut Podstawowych Problemów Techniki PAN ; Komitet Akustyki PAN ; Polskie Towarzystwo Akustyczne
• Czasopismo: Archives of Acoustics
• Rocznik: 2021
• Tom: Vol. 46, No. 4
• Strony: 623--635
• Opis fizyczny: Bibliogr. 64 poz., rys., wykr.

Twórcy

autor

Singh Baljeet

• Department of Mathematics, Post Graduate Government College Sector 11, Chandigarh, 160011, India

autor

Sangwan Asha

• Department of Mathematics, Government College Sampla, Rohtak, 124001, Haryana, India

autor

Singh Jagdish

• Department of Mathematics, Maharshi Dayanand University Rohtak, 124001, Haryana, India

Bibliografia

• 1. Achenbach J.D. (1973), Wave Propagation in Elastic Solids, Vol. 16, North-Holland Publishing Company, Elsevier, Amsterdam.
• 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, doi: 10.1016/0165-2125(84)90029-5.
• 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 10.1016/0020-7225(94)00106-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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 10.1007/BF01696256.
• 24. Iesan D. (2006), On the microstretch piezoelectricity, International Journal of Engineering Science, 44(13-14): 819-829, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 10.1051/jphysrad:01958001905052300.
• 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 10.1090/qam/99708.
• 43. Singh B. (2010), Wave propagation in a prestressed piezoelectric half-space, Acta Mechanica, 211(3): 337-344, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 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, doi: 10.1016/j.rinp.2018.11.045.
• 58. Zenkour A.M., Alghanmi R.A. (2020), Static response of sandwich plates with FG core and piezoelectric faces under thermo-electro-mechanical loads and resting on elastic foundations, Thin-Walled Structures, 157: 107025, doi: 10.1016/j.tws.2020.107025.
• 59. Zenkour A.M., Aljadani M.H. (2019), Porosity effect on thermal buckling behavior of actuated functionally graded piezoelectric nanoplates, European Journal of Mechanics-A/Solids, 78: 103835, doi: 10.1016/j.euromechsol.2019.103835.
• 60. Zenkour A.M., Aljadani M.H. (2020), Buckling analysis of actuated functionally graded piezoelectric plates via a quasi-3D refined theory, Mechanics of Materials, 151: 103632, doi: 10.1016/j.mechmat.2020.103632.
• 61. Zenkour A.M., Hafed Z.S. (2019), Hygro-thermo-mechanical bending of FG piezoelectric plates using quasi-3D shear and normal deformations theory, Latin American Journal of Solids and Structures, 16(7): e218, doi: 10.1590/1679-78255396.
• 62. Zenkour A.M., Hafed Z.S. (2020a), Bending analysis of functionally graded piezoelectric plates via quasi-3D trigonometric theory, Mechanics of Advanced Materials and Structures, 27(18): 1551-1562, 10.1080/15376494.2018.1516325.
• 63. Zenkour A.M., Hafed Z.S. (2020b), Bending response of functionally graded piezoelectric plates using a two-variable shear deformation theory, Advances in Aircraft and Spacecraft Science, 7(2): 115-134, doi: 10.12989/aas.2020.7.2.115.
• 64. Zhilin P.A., Kolpakov Y.E. (2005), A micro-polar theory for piezoelectric materials, [In:] Proceedings of the Advanced Problems in Mechanics, Lecture at XXXIII Summer School -Conference, St. Petersburg, Russia, http://mathenglish.ru/mechanics/zhilin/zhilin8.pdf.