The governing equations of two-temperature generalized magneto-thermoelasticity with hydrostatic initial stress are specialized in two dimensions and are solved for surface wave solutions. The appropriate solutions in a half-space are obtained which satisfy relevant radiation condition and boundary conditions at thermally insulated as well as isothermal surface. The frequency equation of Rayleigh wave is obtained. The frequency equation is also reduced for limiting cases of small thermal coupling and small reduced frequency. Velocity of propagation and amplitude-attenuation factor of Rayleigh wave are computed for a numerical example. To illustrate the dependence of velocity and amplitude-attenuation factor upon two-temperature parameter, initial stress parameter thermal relaxation time and magnetic field, the numerical results are shown graphically.
References
1.
Lord
, H.
, and Shulman
, Y.
, 1967
, “A Generalised Dynamical Theory of Thermoelasticity
,” J. Mech. Phys. Solids
, 15
(5
), pp. 299
–309
.2.
Green
, A. E.
, and Lindsay
, K. A.
, 1972
, “Thermoelasticity
,” J. Elast.
, 2
(1
), pp. 1
–7
.3.
Hetnarski
, R. B.
, and Ignaczak
, J.
, 1999
, “Generalized Thermoelasticity
,” J. Therm. Stresses
, 22
(4–5), pp. 451
–476
.4.
Ignaczak
, J.
, and Ostoja-Starzewski
, M.
, 2009
, Thermoelasticity With Finite Wave Speeds
, Oxford University Press
, Oxford, UK.5.
Montanaro
, A.
, 1999
, “On Singular Surfaces in Isotropic Linear Thermoelasticity With Initial Stress
,” J. Acoust. Soc. Am.
, 106
(3
), pp. 1586
–1588
.6.
Singh
, B.
, Kumar
, A.
, and Singh
, J.
, 2006
, “Reflection of Generalized Thermoelastic Waves From a Solid Half-Space Under Hydrostatic Initial Stress
,” Appl. Math. Comput.
, 177
, pp. 170
–177
.7.
Othman
, M. I. A.
, and Song
, Y.
, 2007
, “Reflection of Plane Waves From an Elastic Solid Half-Space Under Hydrostatic Initial Stress Without Energy Dissipation
,” Int. J. Solids Struct.
, 44
(17
), pp. 5651
–5664
.8.
Singh
, B.
, 2008
, “Effect of Hydrostatic Initial Stresses on Waves in a Thermoelastic Solid Half-Space
,” Appl. Math. Comp.
, 198
(2
), pp. 494
–505
.9.
Singh
, B.
, 2010
, “Wave Propagation in an Initially Stressed Transversely Isotropic Thermoelastic Solid Half-Space
,” Appl. Math. Comp.
, 217
(2
), pp. 705
–715
.10.
Abbas
, I. A.
, and Othman
, M. I.
, 2012
, “Generalized Thermoelastic Interaction in a Fiber-Reinforced Anisotropic Half-Space Under Hydrostatic Initial Stress
,” J. Vib. Control
, 18
(2
), pp. 175
–182
.11.
Othman
, M. I.
, and Atwa
, S. Y.
, 2012
, “Thermoelastic Plane Waves for an Elastic Solid Half-Space Under Hydrostatic Initial Stress of Type III
,” Meccanica
, 47
(6
), pp. 1337
–1347
.12.
Abouelregal
, A. E.
, 2017
, “Fibre-Reinforced Generalized Anisotropic Thick Plate With Initial Stress Under the Influence of Fractional Thermoelasticity Theory
,” Adv. Appl. Math. Mech.
, 9
(3
), pp. 722
–741
.13.
Chen
, P. J.
, and Gurtin
, M. E.
, 1968
, “On a Theory of Heat Conduction Involving Two Temperatures
,” Z. Angew. Math. Phys.
, 19
(4
), pp. 614
–627
.14.
Chen
, P. J.
, and Williams
, W. O.
, 1968
, “A Note on Non-Simple Heat Conduction
,” Z. Angew. Math. Phys.
, 19
(6
), pp. 969
–970
.15.
Chen
, P. J.
, Gurtin
, M. E.
, and Williams
, W. O.
, 1969
, “On the Thermodynamics of Non-Simple Elastic Materials With Two Temperatures
,” Z. Angew. Math. Phys.
, 20
(1
), pp. 107
–112
.16.
Boley
, B. A.
, and Tolins
, I. S.
, 1962
, “Transient Coupled Thermoelastic Boundary Value Problems in the Half-Space
,” ASME J. Appl. Mech.
, 29
(4
), pp. 637
–646
.17.
Warren
, W. E.
, and Chen
, P. J.
, 1973
, “Wave Propagation in the Two Temperature Theory of Thermoelasticity
,” Acta Mech.
, 16
(1–2
), pp. 21
–33
.18.
Puri
, P.
, and Jordan
, P. M.
, 2006
, “On the Propagation of Harmonic Plane Waves Under the Two-Temperature Theory
,” Int. J. Eng. Sci.
, 44
(17
), pp. 1113
–1126
.19.
Youssef
, H. M.
, 2006
, “Theory of Two-Temperature Generalized Thermoelasticity
,” IMA J. Appl. Math.
, 71
(3
), pp. 383
–390
.20.
Magana
, A.
, and Quintanilla
, R.
, 2009
, “Uniqueness and Growth of Solutions in Two-Temperature Generalized Thermoelastic Theories
,” Math. Mech. Solids
, 14
(7
), pp. 622–634.21.
Abbas
, I. A.
, and Youssef
, H. M.
, 2009
, “Finite Element Analysis of Two-Temperature Generalized Magneto-Thermoelasticity
,” Arch. Appl. Mech.
, 79
(10
), pp. 917
–925
.22.
Youssef
, H. M.
, 2011
, “Theory of Two-Temperature Thermoelasticity Without Energy Dissipation
,” J. Therm. Stresses
, 34
(2
), pp. 138
–146
.23.
El-Karamany
, A. S.
, and Ezzat
, M. A.
, 2011
, “On the Two-Temperature Green-Naghdi Thermoelasticity Theories
,” J. Therm. Stresses
, 34
(12
), pp. 1207
–1226
.24.
Ezzat
, M. A.
, and El-Karamany
, A. S.
, 2011
, “Two-Temperature Theory in Generalized Magneto-Thermoelasticity With Two Relaxation Times
,” Meccanica
, 46
(4
), pp. 785
–794
.25.
Ezzat
, M. A.
, and El-Karamany
, A. S.
, 2011
, “Fractional Order Heat Conduction Law in Magneto-Thermoelasticity Involving Two Temperatures
,” Z. Angew. Math. Phys.
, 62
(5
), pp. 937
–952
.26.
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
,” Nucl. Eng. Des.
, 252
, pp. 267
–277
.27.
Sur
, A.
, and Kanoria
, M.
, 2012
, “Fractional Order Two-Temperature Thermoelasticity With Finite Wave Speed
,” Acta Mech.
, 223
(12
), pp. 2685
–2701
.28.
Youssef
, H. M.
, and Elsibai
, K. A.
, 2015
, “On the Theory of Two-Temperature Thermoelasticity Without Energy Dissipation of Green-Naghdi Model
,” Appl. Anal.
, 94
(10
), pp. 1997
–2010
.29.
Ezzat
, M. A.
, El-Karamany
, A. S.
, and El-Bary
, A. A.
, 2016
, “Generalized Thermoelasticity With Memory-Dependent Derivatives Involving Two Temperatures
,” Mech. Adv. Mater. Struct.
, 25
(5
), pp. 545
–553
.30.
Mukhopadhyay
, S.
, Picard
, R.
, Trostorff
, S.
, and Waurick
, M.
, 2017
, “A Note on a Two-Temperature Model in Linear Thermoelasticity
,” Math. Mech. Solids
, 22
(5
), pp. 905
–918
.31.
Abbas
, I. A.
, and Youssef
, H. M.
, 2013
, “Two-Temperature Generalized Thermoelasticity Under Ramp-Type Heating by Finite Element Method
,” Meccanica
, 48
(2
), pp. 331
–339
.32.
Abd-Alla
, A. N.
, and Abbas
, I. A.
, 2002
, “A Problem of Generalized Magneto-Thermoelasticity for an Infinitely Long Perfectly Conducting Cylinder
,” J. Therm. Stresses
, 25
(11
), pp. 1009
–1025
.33.
Abbas
, I. A.
, 2014
, “A Problem on Functional Graded Material Under Fractional Order Theory of Thermoelasticity
,” Theor. Appl. Fract. Mech.
, 74
, pp. 18
–22
.34.
Kumar
, R.
, and Abbas
, I. A.
, 2013
, “Deformation Due to Thermal Source in Micropolar Thermoelastic Media With Thermal and Conductive Temperatures
,” J. Comput. Theor. Nanosci.
, 10
(9
), pp. 2241
–2247
.35.
Ezzat
, M. A.
, El-Karamany
, A. S.
, and El-Bary
, A. A.
, 2018
, “Two-Temperature Theory in Green-Naghdi Thermoelasticity With Fractional Phase-Lag Heat Transfer
,” Microsyst. Tech.
, 24
(2
), pp. 951
–961
.36.
Kumar
, R.
, and Mukhopadhyay
, S.
, 2010
, “Effects of Thermal Relaxation Time on Plane Wave Propagation Under Two-Temperature Thermoelasticity
,” Int. J. Eng. Sci.
, 48
(2
), pp. 128
–139
.37.
Singh
, B.
, and Bala
, K.
, 2012
, “Reflection of P and SV Waves From the Free Surface of a Two-Temperature Thermoelastic Solid Half-Space
,” J. Mech. Mater. Struct.
, 7
(2
), pp. 183
–193
.38.
Prasad
, R.
, and Mukhopadhyay
, S.
, 2012
, “Effects of Rotation on Harmonic Plane Waves Under Two-Temperature Thermoelasticity
,” J. Therm. Stresses
, 35
(11
), pp. 1037
–1055
.39.
Kumar
, A.
, Kant
, S.
, and Mukhopadhyay
, S.
, 2017
, “An In-Depth Investigation on Plane Harmonic Waves Under Two-Temperature Thermoelasticity With Two Relaxation Parameters
,” Math. Mech. Solids
, 22
(2
), pp. 191
–209
.40.
Rayleigh
, L.
, 1885
, “On Waves Propagated Along the Plane Surface of an Elastic Solid
,” Proc. Lond. Math. Soc.
, 17
, pp. 4
–11
.41.
Lockett
, F. J.
, 1958
, “Effect of Thermal Properties of a Solid on the Velocity of Rayleigh Waves
,” J. Mech. Phys. Solids
, 7
(1
), pp. 71
–75
.42.
Deresiewicz
, H.
, 1961
, “A Note on Thermoelastic Rayleigh Waves
,” J. Mech. Phys. Solids
, 9
(3
), pp. 191
–195
.43.
Nayfeh
, A.
, and Nemat-Nasser
, S.
, 1971
, “Thermoelastic Waves in Solids With Thermal Relaxation
,” Acta Mech.
, 12
(1–2
), pp. 53
–69
.44.
Carroll
, M. M.
, 1974
, “A Note on Thermoelastic Surface Waves
,” Mech. Res. Comm.
, 1
(2
), pp. 61
–65
.45.
Agarwal
, V. K.
, 1978
, “On Surface Waves in Generalized Thermoelasticity
,” J. Elast.
, 8
(2
), pp. 171
–177
.46.
Dawn
, N. C.
, and Chakraborty
, S. K.
, 1988
, “On Rayleigh Waves in Green-Lindsay's Model of Generalized Thermoelastic Media, Indian
,” J. Pure Appl. Math.
, 20
(3), pp. 276
–283
.https://www.insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a6f_276.pdf47.
Singh
, B.
, Kumari
, S.
, and Singh
, J.
, 2012
, “On Rayleigh Wave in Generalized Magneto-Thermoelastic Media With Hydrostatic Initial Stress
,” Bull. Pol. Acad. Sci., Tech. Sci.
, 60
(2
), pp. 349
–352
.48.
Singh
, B.
, 2013
, “Propagation of Rayleigh Wave in a Two-Temperature Generalized Thermoelastic Solid Half-Space
,” ISRN Geophys.
, 2013
, p. 857937
.49.
Singh
, B.
, and Bala
, K.
, 2013
, “On Rayleigh Wave in Two-Temperature Generalized Thermoelastic Medium Without Energy Dissipation
,” Appl. Math.
, 4
(1
), pp. 107
–112
.50.
Kumari
, S.
, and Singh
, B.
, 2016
, “Propagation of Rayleigh Surface Wave in a Two-Temperature Thermoelastic Solid Half-Space With Diffusion
,” J. Adv. Appl. Math.
, 1
(3
), pp. 195
–202
.51.
Singh
, B.
, Kumari
, S.
, and Singh
, J.
, 2017
, “Propagation of Rayleigh Wave in Two-Temperature Dual-Phase-Lag Thermoelasticity
,” Mech. Mech. Eng.
, 21
(1
), pp. 105
–116
.http://www.kdm.p.lodz.pl/articles/2017/21_1_10.pdf52.
Biswas
, S.
, and Abo-Dahab
, S. M.
, 2018
, “Effect of Phase-Lags on Rayleigh Wave Propagation in Initially Stressed Magneto-Thermoelastic Orthotropic Medium
,” Appl. Math. Modell.
, 59
, pp. 713
–727
.53.
Passarella
, F.
, Tibullo
, V.
, and Viccione
, G.
, 2017
, “Rayleigh Waves in Isotropic Strongly Elliptic Thermoelastic Materials With Microtemperatures
,” Meccanica
, 52
(13
), pp. 3033
–3041
.54.
Singh
, B.
, 2017
, “Rayleigh Surface Wave in a Porothermoelastic Solid Half-Space
,” Poromechanics-VI, ASCE
, Paris, France
, July 9–13
, pp. 1706
–1713
.55.
Shaw
, S.
, and Othman
, M. I. A.
, 2019
, “Characteristics of Rayleigh Wave Propagation in Orthotropic Magneto-Thermoelastic Half-Space: An Eigen Function Expansion Method
,” Appl. Math. Modell.
, 67
, pp. 605
–620
.Copyright © 2019 by ASME
You do not currently have access to this content.
