Structural Engineering and Mechanics

  • 제85권3호
  • /
  • Pages.305-314
  • /
  • 2023
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Transmission/reflection phenomena of waves at the interface of two half-space mediums with nonlocal theory

  • Adnan, Jahangir (Department of Mathematics, COMSATS University Islamabad) ;
  • Abdul, Waheed (Department of Mathematics, COMSATS University Islamabad) ;
  • Ying, Guo (School of Civil Engineering, Henan University of Science and Technology)
  • 투고 : 2022.09.17
  • 심사 : 2023.01.06
  • 발행 : 2023.02.10
⟨ 이전 논문 다음 논문 ⟩

초록

The article is about the theoretical analysis of the transmission and reflection of elastic waves through the interface of perfectly connected materials. The solid continuum mediums considered are piezoelectric semiconductors and transversely isotropic in nature. The connection among the mediums is considered in such a way that it holds the continuity property of field variables at the interface. The concept of strain and stress introduced by non-local theory is also being involved to make the study more applicable It is found that, the incident wave results in the generation of four reflected and three transmitted waves including the thermal and elastic waves. The thermal waves generated in the medium are encountered by using the concept of three phase lag heat model along with fractional ordered time thermoelasticity. The results obtained are calculated graphically for a ZnO material with piezoelectric semiconductor properties for medium M1 and CdSc material with transversely isotropic elastic properties for medium M2. The influence of fractional order parameter, non-local parameter, and steady carrier density parameter on the amplitude ratios of reflected and refraction waves are studied graphically by MATLAB.

키워드

참고문헌

  1. Aatef, H. and Ibrahim, A. (2021), "A GN model of thermoelastic interaction in a 2D orthotropic material due to pulse heat flux", Struct. Eng. Mech., 80, 669-675. https://doi.org/10.12989/sem.2021.80.6.669.
  2. Abbas, I. and Zenkour, A.M. (2014), "Dual Phase Lag model on thermoelastic interactions in a semi-infinite medium subjected to a ramp type heating", J. Comput. Theor. Nanosci., 11, 642-645. https://doi.org/10.1166/jctn.2014.3407.
  3. Abouelregal, A.E. (2020), "On Green and Naghdi thermoelasticity model without energy dissipation with higher-order time differential and phase-lags", J. Appl. Compos. Mech., 6, 445-456. https://doi.org/10.22055/jacm.2019.29960.1649.
  4. Ahmed, E.A. and Marin, M. (2020), "The size-dependent thermoelastic vibrations of nanobeams subjected to harmonic excitation and rectified sine wave heating", Math., 8(7), 1128. https://doi.org/10.3390/math8071128.
  5. Biot, M.A (1956), "Thermoclasticity and irreversible thermodynamics", J. Appl. Phys., 27, 240-253. https://doi.org/10.1063/1.1722351.
  6. Cao, X., Hu, S., Liu, J. and Shi, J. (2019), "Generalized Rayleigh surface waves in a piezoelectric semiconductor half space", Meccanica, 54, 271-281. https://doi.org/10.1007/s11012-019-00944-1.
  7. Chandrasekharaiah, D.S. (1986), "Thermoelasticity with second sound: A review", Appl. Mech. Rev., 39, 355-376. https://doi.org/10.1115/1.3143705.
  8. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10, 425-435. https://doi.org/10.1016/0020-7225(72)90050-X.
  9. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  10. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  11. Ezzat, M.A. and El-Karamany A.S. (2011), "Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures", Zeitschrift fur angewandte Mathematik und Physik, 62, 937-952. https://doi.org/10.1007/s00033-011-0126-3.
  12. Ezzat, M.A. and El-Karamany A.S. (2011), "Theory of fractional order in Electro-thermoelasticity", Eur. J. Mech. A/Solid., 30, 491-500. https://doi.org/10.1016/j.euromechsol.2011.02.004.
  13. Ezzat, M.A., El-Karamany, A.S. and Ezzat, S.M. (2012), "Two temperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer", J. Nucl. Eng. Des., 252, 267-277. https://doi.org/10.1016/j.nucengdes.2012.06.012.
  14. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2, 1-7. https://doi.org/10.1007/BF00045689.
  15. Guo, X., Wei, P., Li, L. and Tang, Q. (2015), "Influences of mechanically and dielectrically imperfect interfaces on the reflection and transmission waves between two piezoelectric half spaces", Int. J. Solid. Struct., 63, 184-205. https://doi.org/10.1016/j.ijsolstr.2015.02.050.
  16. Hutson, A.R. and White, D.L. (1962), "Elastic wave propagation in piezoelectric semiconductors", J. Appl. Phys., 33, 40-47. https://doi.org/10.1063/1.1728525.
  17. Ibrahim, A. (2014), "A GN model based upon two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity", Appl. Math. Comput., 245, 108-115. https://doi.org/10.1016/j.amc.2014.07.059.
  18. Ibrahim, A. (2015), "Analytical solution for a free vibration of a thermoelastic hollow sphere", Mech. Bas. Des. Struct. Mach., 43, 265-276. https://doi.org/10.1080/15397734.2014.956244.
  19. Ibrahim, A. (2015), "Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity", Appl. Math. Model., 39, 6196-6206. https://doi.org/10.1016/j.apm.2015.01.065.
  20. Iqbal, K., Parveen, l. and Kulvinder, S. (2021), "Reflection of plane harmonic wave in rotating media with fractional order heat transfer and two temperatures", Part. Diff. Equ. Appl. Math., 4, 10049. https://doi.org/10.1016/j.padiff.2021.100049.
  21. Iqbal, K., Parveen, L. and Kulvinder, S. (2022), "Thermoelastic damping in generalized simply supported piezo-thermo-elastic nanobeam", Struct. Eng. Mech., 81, 29-37. https://doi.org/10.12989/sem.2022.81.1.029.
  22. Jiao, F., Wei, P., Zhou, Y. and Zhou, X. (2019), "Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-space", Eur. J. Mech/Solid., 75, 70-81. https://doi.org/10.1016/j.euromechsol.2019.01.007.
  23. Ke, L. and Wang, Y.S. (2012), "Thermo-electric-mechanical vibration of the piezoelectric nanobeams based on the nonlocal theory", Smart Mater. Struct., 21, 1-12. https://doi.org/10.1088/0964-1726/21/2/025018.
  24. Lijun, Z., Bhatti, M.M., Efstathios, E.M., Marin, M. and Ellahi, R. (2022), "Hybrid nanofluid flow towards an elastic surface with tantalum and nickel nanoparticles, under the influence of an induced magnetic field", Eur. Phys. J. Spec. Topic., 231, 521-533. https://doi.org/10.1140/epjs/s11734-021-00409-1.
  25. Liu, C., Ke, L., Wang, Y.S. and Kitipornchai, S. (2013), "Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory", Compos. Struct., 106, 167-174. https://doi.org/10.1016/j.compstruct.2013.05.031.
  26. Lord, H. and Shulman, Y.A. (1967), "generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  27. Ma, L.H., Ke, L.L., Wang, Y.Z. and Wang, Y.S. (2017), "Wave Propagation analysis of piezoelectric nanoplates based on the nonlocal theory", Int. J. Struct. Stab. Dyn., 18, 1-19. https://doi.org/10.1142/S0219455418500608.
  28. Mcfee, J.H. (1966), "Transmission and amplification of acoustic waves in piezoelectric semiconductors", Phys. Acoustst., 4, 1-45. https://doi.org/10.1016/B978-0-12-395663-7.50012-1.
  29. Mindlin, R.D. (1961), "On the equations of motion of piezoelectric crystals", Prob. Contin. Mech., 282-290. https://doi.org/10.4236/crcm.2013.29135.
  30. Mindlin, R.D. (1974), "Equations of high-frequency vibrations of thermo-piezoelectric crystal plates", Int. J. Solid. Struct., 10, 625-637. https://doi.org/10.1016/0020-7683(74)90047-X.
  31. Minjie, W., Kuihua, W., Wu. J. and Houren, X. (2020), "Nonlocal thermo-hydro mechanical (THM) coupling dynamics response of saturated porous thermoelastic media with temperature-dependent physical properties", Wave. Random Complex Media., 1-23. https://doi.org/10.1080/17455030.2021.1954262.
  32. Parveen, L. and Himanshi. (2022), "Fractional effect in an orthotropic magneto-thermoelastic rotating solid of type GN-II due to normal force", Struct. Eng. Mech., 81, 503-511. https://doi.org/10.12989/sem.2022.81.4.503.
  33. Roychoudhuri, S.K. (2007), "On thermo elastic three-phase-lag model", J. Therm. Stress., 30, 231-238. https://doi.org/10.1080/0149573060 1130919.
  34. Sangwan, A., Singh, B. and 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/10.1016/j.joes.2019.04.006.
  35. Sanjeev, A., Sonal, N. and Somali, M. (2020), "Reflection and transmission of quasi plane waves at the interface of piezoelectric semiconductor with initial stress", Appl. Math. Mech., 41(1), 1-18. https://doi.org/10.1007/s10483-021-2738-9.
  36. Sharma, J.N. Kumar, V. and Dayal, C. (2003), "Reflection of generalized thermoelastic waves from the boundary of a half-space", J. Therm. Stress., 26, 925-942. https://doi.org/10.1080/01495730306342.
  37. Sharma, K. and Marin, M. (2014), "Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids", Analele Universitatii" Ovidius" Constanta-Seria Matematica, 22(2), 151-176. https://doi.org/10.2478/auom-2014-0040.
  38. Sharmaa, J.N., Mohinder, P. and Dayal, C. (2005), "Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials", J. Sound Vib., 284, 227-248. https://doi.org/10.1016/j.jsv.2004.06.036.
  39. Siddhartha, B. (2021), "The propagation of plane waves in nonlocal visco-thermoelastic porous medium based on nonlocal strain gradient theory", Wave. Random Complex Media, 1-32. https://doi.org/10.1080/17455030.2021.1909780.
  40. Xinli, X., Chunwei, Z., Farayi, M., Sebaey, T. and Afrasyab, K. (2021), "Wave propagation analysis of porous functionally graded curved beams in the thermal environment", Struct. Eng. Mech., 79, 665-675. https://doi.org/10.12989/sem.2021.79.6.665.
  41. Youssef, H.M. (2010), "Theory of fractional order generalized thermoelasticity", J. Heat Trans., 132, 1-7. https://doi.org/10.1115/1.4000705.
  42. Zenkour, A.M. (2018), "Refined micro-temperatures multi-phase-lags theory for plane wave propagation in thermoelastic medium", Result. Phys., 11, 929-937. https://doi.org/10.1016/j.rinp.2018.10.030.
  43. Zenkour, A.M. (2019), "Refined multi-phase-lags theory for photo thermal waves of a gravitated semiconducting half-space", Compos. Struct., 212(5), 346-364. https://doi.org/10.1016/j.compstruct.2019.01.015.