Abstract
The present study is concerned with the reflection and propagation of thermoelastic harmonic plane waves from the stress-free and isothermal surface of a homogeneous, isotropic thermally conducting elastic half-space in the frame of the modified Green–Lindasy (MGL) theory of generalized thermoelasticity with strain rate proposed by Yu et al. (Meccanica 53:2543–2554, 2018). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear-type (SV-type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios of the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds and the amplitude ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the GL and LS models.
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References
M Biot J. Appl. Phys. 27 240 (1956)
H W Lord and Y Shulman J. Mech. Phys. Solids 15 299 (1967)
C Cattaneo Comptes. Rendus. Acad. Sci. 2 431 (1958)
A E Green and K A Lindsay J. Elast. 2 1 (1972)
A E Green and P M Naghdi Proc. R. Soc. Lond. A 432 171 (1991)
A E Green and P M Naghdi J. Therm. Stresses 15 253 (1992)
A E Green and P M Naghdi J. Elast. 31 189 (1993)
M Marin Acta Mech 122 155 (1997)
H H Sherief, A M A El-Sayed and A M A El-Latief Int. J. Solids Struct. 47 269 (2010)
H M Youssef J. Heat Trans. 132 61301-1 (2010)
Y Z Povstenko J. Therm. Stresses 34 97 (2011)
Y J Yu, W Hu and X-G Tian Int. j. Eng. Sci. 81 123 (2014)
M Bachher, N Sarkar and A Lahiri Int. J. Mech. Sci. 89 84 (2014)
Y J Yu, X-G Tian and Q-L Xion Eur. J. Mech. A Solids 60 238 (2016)
Y J Yu, Z-N Xu, C-L Li and X-G Tian Compos. Struct. 146 108 (2016)
M Marin Contin. Mech. Thermodyn. 29 1365 (2017)
K Lotfy, R Kumar and W Hassan Appl. Math. Mech. Engl. Ed. 39 783 (2018)
K Lotfy Sci. Rep. 9 3319 (2019)
K Lotfy Wave Random. Complex (2019) https://doi.org/10.1080/17455030.2019.1580402
Y J Yu, Z-N Xue and X-G Tian Meccanica 53 2543–2554 (2018)
R Quintanilla Meccanica 53 3607 (2018)
P Chadwick and I N Sneddon J. Mech. Phys. Solids 6 223 (1958)
A H Nayfeh and S Nemat-Nasser Acta Mech. 12 53 (1971)
P Puri Int. J. Eng. Sci. 11 735 (1973)
V K Agarwal Acta Mech. 34 185 (1979)
S K Roychoudhuri and S Mukhopadhyay Int. J. Math. Math. Sci. 23 497 (2000)
S B Sinha and K A Elsibai J. Therm. Stresses 20 129 (1997)
J N Sharma, V Kumar and D Chand J. Therm. Stresses 26 925 (2003)
M I A Othman and Y Q Song Acta Mech. 184 189 (2006)
M I A Othman and Y Q Song Int. J. Solids Struct. 44 5651 (2007)
N D Gupta, A Lahiri and N C Das Math. Mech. Solids17 543 (2011)
S M Abo-Dahab Can. J. Phys. 93 1 (2015)
S Biswas and N Sarkar Mech. Mater. 126 140 (2018)
Y Li, W Wang, P Wei and C Wang Meccanica 53 2921 (2018)
N Sarkar and S K Tomar J. Therm. Stresses42 580 (2019)
S Mondal, N Sarkar and N Sarkar J. Therm. Stresses42 1035 (2019)
N Das, N Sarkar and A Lahiri Appl. Math. Model.73 526 (2019)
K Lotfy, S M Abo-Dahab and R Tantawy Silicon (2019) https://doi.org/10.1007/s12633-019-00116-6
D S Chandrasekharaiah Mech. Res. Commun. 23 549 (1996)
V K Agarwal Acta Mech. 34 181 (1979)
S K Roychoudhuri J. Elast. 15 59 (1985)
J N Sharma, D Grover and D Kaur Appl. Math. Model. 35 3396 (2011)
J D Achenbach Wave Propagation in Elastic Solids (New York: North-Holland) (1976)
M C Singh and N Chakraborty Appl. Math. Model. 37 463 (2013)
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Sarkar, N., De, S. & Sarkar, N. Modified Green–Lindsay model on the reflection and propagation of thermoelastic plane waves at an isothermal stress-free surface. Indian J Phys 94, 1215–1225 (2020). https://doi.org/10.1007/s12648-019-01566-9
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DOI: https://doi.org/10.1007/s12648-019-01566-9