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Effect of Two Temperatures and Stiffness on Waves Propagating at the Interface of Two Micropolar Thermoelastic Media

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This paper is concerned with the effect of two temperatures and stiffness on wave propagation at the interface of two micropolar thermoelastic media on the basis of the thermoelasticity theory of type III (Green–Naghdi, or GN, model). The amplitude ratios of various reflected and transmitted waves are obtained for an imperfect boundary. The effect of the normal force stiffness, transverse force stiffness, transverse couple stiffness, thermal conductivity, and two temperatures on these amplitude ratios is considered for the incidence of various plane waves. The variations of the amplitude ratios with the angle of incidence are shown graphically.

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References

  1. A. E. Green and P. M. Naghdi, A re-examination of the basic postulates of thermomechanics, Proc. R. Soc. London A, 357, 253–270 (1991).

    Article  MathSciNet  Google Scholar 

  2. A. E. Green and P. M. Naghdi, On undamped heat waves in an elastic solid, J. Therm. Stresses, 15, 253–264 (1992).

    Article  MathSciNet  Google Scholar 

  3. A. E. Green and P. M. Naghdi, Thermoelasticity without energy dissipation, J. Elast., 31, 189–209 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. C. Eringen, Linear theory of micropolar elasticity, J. Appl. Math. Mech., 15, 909–923 (1966).

    MATH  MathSciNet  Google Scholar 

  5. A. C. Eringen, Foundations of Micropolar Thermoelasticity, Int. Centre Mech. Sci., Udline Course and Lectures 23, Springen-Verlag, Berlin (1970).

    Book  MATH  Google Scholar 

  6. W. Nowacki, Theory of Asymmetric Elasticity, Pergamon Press, Oxford (1986).

    MATH  Google Scholar 

  7. A. C. Eringen, Microcontinuum Field Theories I, Foundations and Solids, Springer-Verlag, Berlin (1999).

    Book  MATH  Google Scholar 

  8. D. S. Chandrasekharaiah, Heat flux dependent micropolar thermoelasticity, Int. J. Eng. Sci., 24, 1389–1395 (1986).

    Article  MATH  Google Scholar 

  9. E. Boschi and D. Iesan, A generalized theory of linear micropolar thermoelasticity, Meccanica, 7, 154–157 (1973).

    Article  Google Scholar 

  10. P. J. Chen, M. E. Gurtin, and W. O. Williams, A note on nonsimple heat conduction, ZAMP, 19, 960–970 (1968).

    Google Scholar 

  11. P. J. Chen, M. E. Gurtin, and W. O. Williams, On the thermoelastic material with two temperatures, ZAMP, 20, 107–112 (1969).

    Article  MATH  Google Scholar 

  12. M. Boley, Thermoelastic and irreversible thermodynamics, J. Appl. Phys., 27, 240–253 (1956).

    Article  MathSciNet  Google Scholar 

  13. W. E. Warren and P. J. Chen, Wave propagation in the two-temperature theory of thermoelasticity, Acta Mech., 16, 21–23 (1973).

    Article  MATH  Google Scholar 

  14. H. M. Youssef, Theory of two-temperature generalized thermoelasticity, IMA J. Appl. Math., 71, 383–390 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  15. R. Kumar and S. Mukhopadhyay, Effect of thermal relaxation time on plane wave propagation under two temperature thermoelasticity, Int. J. Eng. Sci., 48, 128–139 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  16. S. Kaushal, N. Sharma, and R. Kumar, Propagation of waves in generalized thermoelastic continua with two temperatures, Int. J. Appl. Mech. Eng., 15, 1111–1127 (2010).

    Google Scholar 

  17. S. Kaushal, R. Kumar, and A. Miglani, Wave propagation in temperature rate dependent thermoelasticity with two temperatures, Math. Sci., 5, 125–146 (2011).

    MATH  MathSciNet  Google Scholar 

  18. M. A. Ezzat and E. S. Awad, Constitutive relations, uniqueness of solution and thermal shock application in the linear theory of micropolar generalized thermoelasticity involving two temperatures, J. Therm. Stresses, 33, 226–250 (2010).

    Article  Google Scholar 

  19. S. I. Rokhlin and D. Marom, Study of adhesive bonds using low-frequency obliquely incident ultrasonic wave, J. Acoust. Soc. Am., 80, 585–590 (1986).

    Article  Google Scholar 

  20. J. P. Jones and J. P. Whittier, Waves in a flexible bonded interface, J. Appl. Mech., 34, 905–909 (1967).

    Article  Google Scholar 

  21. G. S. Murty, A theoretical model for the attenuation and dispersion of Stonley waves at the loosely bonded interface of elastic half-space, Phys. Earth Planet. Inter., 11, 65–79 (1975).

    Article  Google Scholar 

  22. A. H. Nayfeh and E. M. Nassar, Simulation of the influence of bonding materials on the dynamic behaviour of laminated composites, J. Appl. Mech., 45, 855–828 (1978).

    Google Scholar 

  23. S. I. Rokhlin, M. Hefets, and M. Rosen, An elastic interface wave guided by a thin film between two solids, J. Appl. Phys., 51, 3579–3582 (1980).

    Article  Google Scholar 

  24. S. I. Rokhlin, Adhesive joint characterization by ultrasonic surface and interface waves, in: K. L. Mittal, Ed., Adhesive Joints: Formation, Characteristics and Testing, Plenum, New York (1984), pp. 307–345.

    Chapter  Google Scholar 

  25. A. Pilarski and J. L. Rose, A transverse wave ultrasonic oblique-incidence technique for interface weakness detection in adhesive bonds, J. Appl. Phys., 63, 300–307 (1988).

    Article  Google Scholar 

  26. R. Kumar and N. Sharma, Effect of viscosity on wave propagation between two micropolar viscoelastic thermoelastic solids with two relaxation times having interfacial imperfections, Int. J. Manuf. Sci. Technol., 1, 133–152 (2007).

    MathSciNet  Google Scholar 

  27. R. Kumar, N. Sharma, and P. Ram, Reflection and transmission of micropolar elastic waves at an imperfect boundary, Multidiscip. Model. Mater. Struct., 4, 15–36 (2008).

    Article  Google Scholar 

  28. R. Kumar, N. Sharma, and P. Ram, Response of imperfections at the boundary surface, Int. e-J. Eng. Math. Theory Appl., 3, 90–109 (2008).

    Google Scholar 

  29. R. Kumar, N. Sharma, and P. Ram, Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media, Theor. Appl. Fract. Mech., 49, 305–312 (2008).

    Article  Google Scholar 

  30. R. Kumar, N. Sharma, and P. Ram, Effect of stiffness on reflection and transmission of micropolar thermoelastic waves at an interface between an elastic and micropolar generalized thermoelastic solid, Struct. Eng. Mech., Int. J., 31, 117–135 (2009).

    Article  Google Scholar 

  31. P. Ram and N. Sharma, Reflection and transmission of micropolar thermoelastic waves with an imperfect bonding, Int. J. Appl. Math. Mech., 4, 1–23 (2008).

    Google Scholar 

  32. R. Kumar and N. Sharma, Effect of viscocity and stiffness on wave propagation in micropolar visoelastic media, Int. J. Appl. Mech. Eng., 4, 415–431 (2009).

    Google Scholar 

  33. N. Sharma, S. Kaushal, and R. Kumar, Effect of viscosity and stiffness on amplitude ratios in microstretch viscoelastic media, Appl. Math. Inform. Sci., 5, 321–341 (2011).

    MATH  MathSciNet  Google Scholar 

  34. R. Kumar and V. Chawla, Effect of rotation and stiffness on surface wave propagation in an elastic layer lying over a generalized thermodiffusive elastic half-space with imperfect boundary, J. Solid Mech., 2, 28–42 (2010).

    Google Scholar 

  35. R. Kumar and V. Chawla, Effect of rotation on surface wave propagation in an elastic layer lying over a thermodiffusive elastic half-space having imperfect boundary, Int. J. Appl. Mech. Eng., 16, 37–55 (2011).

    Google Scholar 

  36. R. Kumar and V. Chawla, Wave propagation at the imperfect boundary between transversely isotropic thermodiffusive elastic layer and half-space, J. Eng. Phys. Thermophys., 84, 1192–1200 (2011).

    Article  Google Scholar 

  37. H. Taheri, S. Fariborz, and M. R. Eslami, Thermoelasticity solution of a layer using the Green–Naghdi model, J. Therm. Stresses, 27, 795–809 (2004).

    Article  Google Scholar 

  38. S. Mukhopadhyay and R. Kumar, A problem on thermoelastic interactions in an infinite medium with a cylindrical hole in generalized thermoelasticity III, J. Therm. Stresses, 31, 455–475 (2008).

    Article  Google Scholar 

  39. N. A. Mohamed, A. E. Khaled, and E. A. Ahmed, Electromagneto-thermoelastic problem in a thick plate using Green and Naghdi theory, Int. J. Eng. Sci., 47, 680–690 (2009).

    Article  MATH  Google Scholar 

  40. S. Chirita and M. Ciarletta, On the harmonic vibrations in linear thermoelasticity without energy dissipation, J. Therm. Stresses, 33, 858–878 (2010).

    Article  Google Scholar 

  41. F. Passarella and V. Zampoli, Reciprocal and variational principles in micropolar thermoelasticity of type II, Acta Mech., 216, 29–36 (2011).

    Article  MATH  Google Scholar 

  42. S. Chirita and M. Ciarletta, Several results in uniqueness and continous dependence in thermoelasticity of type III, J. Therm. Stresses, 34, 873–889 (2011).

    Article  Google Scholar 

  43. A. I. Lavrentyev and S. I. Rokhlin, Ultrasonic spectroscopy of imperfect contact interfaces between a layer and two solids, J. Acoust. Soc. Am., 103, 657–664 (1998).

    Article  Google Scholar 

  44. A. C. Eringen, Plane waves in nonlocal micropolar elasticity, Int. J. Eng. Sci., 22, 1113–1121 (1984).

    Article  MATH  Google Scholar 

  45. R. S. Dhaliwal and A. Singh, Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India (1980).

    Google Scholar 

  46. R. D. Gauthier, Experimental investigations on micropolar media, in: O. Brulin and R. K. T. Hsieh, Eds., Mechanics of Micropolar Media, World Scientific, Singapore (1982).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Kurukshetra University, Kurukshetra, 136119, India

    Rajneesh Kumar

  2. Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana, Punjab, 141008, India

    Mandeep Kaur

Authors
  1. Rajneesh Kumar
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  2. Mandeep Kaur
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Correspondence to Mandeep Kaur.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 88, No. 2, pp. 522–533, March–April, 2015.

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Kumar, R., Kaur, M. Effect of Two Temperatures and Stiffness on Waves Propagating at the Interface of Two Micropolar Thermoelastic Media. J Eng Phys Thermophy 88, 543–555 (2015). https://doi.org/10.1007/s10891-015-1220-8

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  • DOI: https://doi.org/10.1007/s10891-015-1220-8

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