A vector–matrix differential equation is formulated using normal mode analysis from the governing equations of a three-dimensional anisotropic half space in presence of heat source and gravity. The corresponding solution is obtained with the help of eigenvalue approach. Numerical computations for displacement, thermal strain and stress component, temperature distribution are evaluated and presented graphically.
Issue Section:
Technical Brief
Keywords:
Thermal stress
References
1.
Biot
, M. A.
, 1956
, “Thermoelasticity and Irreversible Thermodynamics
,” J. Appl. Phys.
, 27
(3
), pp. 240
–253
.2.
Lord
, H. W.
, and Shulman
, Y.
, 1967
, “A Generalized Dynamical Theory of Thermoelasticity
,” J. Mech. Phys. Solids
, 15
(5
), pp. 299
–309
.3.
Green
, A. E.
, and Lindsay
, K. A.
, 1972
, “Thermoelasticity
,” J. Elasticity
, 2
(1
), pp. 1
–7
.4.
Green
, A. E.
, and Naghdi
, P. M.
, 1993
, “Thermoelasticity Without Energy Dissipation
,” Elasticity
, 31
(3
), pp. 189
–208
.5.
Dhaliwal
, R. S.
, and Sherief
, H. H.
, 1980
, “Generalized Thermoelasticity for Anisotropic Media
,” Q. Appl. Math.
, 33
(1
), pp. 1
–8
. 6.
Sherief
, H. H.
, and Anwar
, M. N.
, 1986
, “Problem in Generalized Thermoelasticity
,” J. Therm. Stresses
, 9
, pp. 165
–181
.7.
Santra
, S.
, Das
, N. C.
, Kumar
, R.
, and Lahiri
, A.
, 2015
, “Three-Dimensional Fractional Order Generalized Thermoelastic Problem Under the Effect of Rotation in a Half-Space
,” J. Therm. Stresses
, 38(3)
, pp. 309
–324
.8.
Bachher
, M.
, Sarkar
, N.
, and Lahiri
, A.
, 2015
, “State-Space Approach to 3D Generalised Thermoviscoelasticity Under Green and Naghdi Theory II
,” Math. Models Eng.
, 1(2)
, pp. 111
–124
.http://www.jve.lt/Vibro/MME-2015-1-2/MME00115120014.html9.
Das
, N. C.
, and Lahir i
, A.
, 2000
, “Thermoelastic Interaction Due to Prescribed Pressure Inside a Spherical Cavity in an Unbounded Medium
,” Indian J. Pure Appl. Math.
, 31
(1
), pp. 1
–35
.10.
Abd-Alla
, A. M.
, Abo-Dahab
, S. M.
, and Al-Mullise
, A.
, 2013
, “Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media Under Four Theories
,” J. Appl. Math.
, 2013
, p. 562369
.11.
Othman
, M. I. A.
, and Lotfy
, K.
, 2013
, “The Effect of Magnetic Field and Rotation of the 2-D Problem of a Fiber-Reinforced Thermoelastic Under Three Theories With Influence of Gravity
,” Mech. Mater.
, 60
, pp. 129
–143
.12.
Othman
, M. I. A.
, and Song
, Y. Q.
, 2006
, “Effect of Rotation on the Reflection of Magneto-Thermoelastic Waves Under Thermoelasticity Without Energy Dissipation
,” Acta Mech.
, 184
(1–4
), pp. 189
–204
.13.
Ezzat
, M. A.
, Othman
, M. I.
, and El-Karamany
, A.
, 2001
, “Electromagnetic-Thermoelastic Plane Waves With Thermal Relaxation in a Medium of Perfect Conductivity
,” J. Therm. Stresses
, 24
(5), pp. 411
–432
.14.
Sarkar
, N.
, and Lahiri
, A.
, 2013
, “The Effect of Gravity Field on Plane Waves in a Fiberreinforced Two Temperature Magneto-Thermoelastic Medium Under Lord-Shulman Theory
,” J. Therm. Stresses
, 36
(9
), pp. 895
–914
.15.
Pal
, P.
, and Kanoria
, M.
, 2017
, “Thermoelastic Wave Propagation in a Transversely Isotropic Thick Plate Under Green–Naghdi Theory Due to Gravitational Field
,” J. Therm. Stresses
, 40
(4
), pp. 470
–485
.16.
Deswal
, S.
, and Hooda
, N.
, 2015
, “A Two-Dimensional Problem for a Rotating Magneto-Thermoelastic Half-Space With Voids and Gravity in a Two-Temperature Generalized Thermoelasticity Theory
,” J. Mech.
, 31
(6
), pp. 639–651.17.
Abd-Alla
, A. M.
, Abo-Dahab
, S. M.
, Hammad
, H. A.
, and Mahmoud
, S. R.
, 2011
, “On Generalized Magneto-Thermoelastic Rayleigh Waves in a Granular Medium Under Influence of Gravity Field and Initial Stress
,” J. Vib. Control
, 17
(1
), pp. 115
–128
.18.
Abouelregal
, A. E.
, and Abo-Dahab
, S. M.
, 2012
, “Dual Phase Lag Model of Magneto-Thermoelasticity Infinite Nonhomogeneous Solid Having a Spherical Cavity
,” J. Therm. Stresses
, 35
(9
), pp. 820
–841
.19.
Abo-Dahab
, S. M.
, and Salama
, M. M.
, 2014
, “A Plane Magnetothermoelastic Waves Reflection and Transmission Between Two Solid Media With External Heat Sources and Initial Stress
,” J. Therm. Stresses
, 37
(9
), pp. 1124
–1151
.20.
Abo-Dahab
, S. M.
, 2015
, “On Magnetic Field and Two Thermal Relaxation Times for p-Waves Propagation at Interface Between Two Solid Liquid Media Under Initial Stress and Heat Sources
,” J. Comput. Theor. Nanosci.
, 12
(3
), pp. 361
–370
.21.
Lofty
, K.
, 2017
, “Photothermal Waves for Two Temperature With a Semiconducting Medium Under Using a Dual-Phase-Lag Model and Hydrostatic Initial Stress
,” Waves Random Complex Media
, 27
(3
), pp. 482
–501
.22.
Lofty
, K.
, 2016
, “The Elastic Wave Motions for a Photothermal Medium of a Dual-Phase-Lag Model With an Internal Heat Source and Gravitational Field
,” Can. J. Phys.
, 94
(4
), pp. 400
–409
.23.
Lofty
, K.
, and Gabr
, M. E.
, 2017
, “Response of a Semiconducting Infinite Medium Under Two Temperature Theory With Photothermal Excitation Due to Laser Pulses
,” Opt. Laser Technol.
, 97
, pp. 198
–208
.24.
Lofty
, K.
, and Hassan
, W.
, 2014
, “Normal Mode Method for Two-Temperature Generalized Thermoelasticity Under Thermal Shock Problem
,” J. Therm. Stresses
, 37
(5
), pp. 545
–560
.25.
Lofty
, K.
, 2017
, “A Novel Solution of Fractional Order Heat Equation for Photothermal Waves in a Semiconductor Medium With a Spherical Cavity
,” Chaos, Solitons Fractals
, 99
, pp. 233
–242
.26.
Kh
, L.
, 2014
, “Two Temperature Generalized Magneto-Thermoelastic Interactions in an Elastic Medium Under Three Theories
,” App. Math. Comp.
, 227
, pp. 871
–888
.27.
Youssef
, H. M.
, and Al-Lehaibi
, E. A.
, 2011
, “Fractional Order Generalized Thermoelastic Infinite Medium With Cylindrical Cavity Subjected to Harmonically Varying Heat
,” Engineering
, 3
(1
), pp. 32
–37
.28.
Lahiri
, A.
, Das
, N. C.
, Sarkar
, S.
, and Das
, M.
, 2009
, “Matrix Method of Solution of Coupled Differential Equations and It's Application to Generalized Thermoelasticity
,” Bull. Calcutta Math. Soc.
, 101
(6
), pp. 571
–590
.29.
Santra
, S.
, Das
, N. C.
, and Lahiri
, A.
, 2017
, “Dynamic Problem in 3D Thermoelastic Half-Space With Rotation in Context of G-N Type II and Type III
,” Math. Models Eng.
, 3
(1
), pp. 58
–70
.30.
Chattopadhaya
, A.
, and Rogerson
, G. A.
, 2001
, “Wave Reflection in Slightly Compressible, Finitely Deformed Elastic Media
,” Arch. Appl. Mech.
, 71
(4–5), pp. 307
–316
.Copyright © 2018 by ASME
You do not currently have access to this content.