In this paper we investigated the propagation of SV-waves under effect of the magnetic field, initial stress and two thermal relaxation times. The problem of reflection and transmission of thermoelastic waves at a solid-liquid interface in presence of initial stress and magnetic field has been investigated subjected to certain boundary conditions. The appropriate expressions to find the amplitudes ratios for the incident wave (SV-waves) have been obtained. The reflection and transmitted coefficients for the incident SV-waves are computed numerically, considering the initial stress, relaxation times, and magnetic field effect and presented graphically. The results indicate that the effects of magnetic field, initial stress and two thermal relaxation times are very pronounced.
Abd-AllaAMAbo-DahabSMBayonesFS (2013) Propagation of Rayleigh waves in magneto-thermo-elastic half-space of a homogeneous orthotropic material under the effect of the rotation, initial stress and gravity field. Journal of Vibration and Control19: 1395–1420.
2.
Abd-AllaAMAbo-DahabSMMahmoudSRHammadHA (2011) On generalized magneto-thermoelastic Rayleigh waves in a granular medium under influence of gravity field and initial stress. Journal of Vibration and Control40: 451–472.
3.
Abd-AllaAMHammadHAAbo-DahabSM (2004) Magneto-thermo-viscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading. Applied Mathematics and Computation155: 235–248.
4.
Abd-AllaAMMahmoudSR (2010) Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model. Meccanica45: 451–462.
5.
Abd-AllaAMMahmoudSRAbo-DahabSM (2012) On problem of transient coupled thermoelasticity of an annular fin. Meccanica47: 1295–1306.
6.
Abd-AllaANYahiaAAAbo-DahabSM (2003) On the reflection of the generalized magneto-thermo-viscoelastic plane waves. Chaos, Solitons & Fractals16: 211–231.
7.
Abo-DahabSM (2010) Propagation of P waves from stress-free surface elastic half-space with voids under thermal relaxation and magnetic field. Applied Mathematical Modelling34: 1798–1806.
8.
Abo-DahabSM (2011) Reflection of P and SV waves from stress-free surface elastic half-space under influence of magnetic field and hydrostatic initial stress without energy dissipation. Journal of Vibration and Control17: 2213–2221.
9.
Abo-Dahab SM (2014) Propagation of Stoneley waves in magneto-thermoelastic materials with voids and two relaxation times. Journal of Vibration and Control, in press.
10.
Abo-DahabSMMohamedRA (2010) Influence of magnetic field and hydrostatic initial stress on reflection phenomena of P and SV waves from a generalized thermoelastic solid half-space. Journal of Vibration and Control16: 685–699.
11.
Abo-DahabSMMohamedRASinghB (2011) Rotation and magnetic field effects on P wave reflection from stress-free surface elastic half-space with voids under one thermal relaxation time. Journal of Vibration and Control1: 1827–1839.
12.
AhmedSMAbo-DahabSM (2010) Propagation of love waves in an orthotropic granular layer under initial stress overlying a semi-infinite granular medium. Journal of Vibration and Control16: 1845–1858.
13.
AngelTCAchenbachJD (1983) Reflection and transmission of elastic waves by a periodic array of crack. Journal of Applied Mechanics52: 33–41.
14.
BeeversCEBreeJ (1975) A note on wave reflection problems in linear thermoelasticity. Journal of Mathematics and Physical Science9: 355–362.
15.
BiotMA (1956) Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics27: 240–253.
16.
ChakrabortyNSinghMC (2011) Reflection and refraction of a plane thermoelastic wave at a solid-solid interface under perfect boundary condition, in presence of normal initial stress. Applied Mathematical Modelling35: 5286–5301.
17.
ChoEGurnisM (2008) Thermally induced brittle deformation in oceanic lithosphere and the spacing of fracture zones. Earth Planet. Science Letter269: 259–270.
18.
DeresiewiczH (1960) Effect of boundaries on waves in a thermoelastic solid: Reflection of plane waves from a plane boundary. Journal of Mech. Phys. Solids8: 164–172.
19.
El-NaggarAMAbd-AllaAM (1987) On a generalized thermoelastic problem in an infinite cylinder under initial stress. Earths, Moon & Planets37: 213–223.
20.
GreenAELindsayA (1972) Thermoelasticity. Journal of Elasticity2: 1–7.
21.
GreenAENaghdiPM (1991) A re-examination of the basic postulate of thermo mechanics. Proc. Roy. Soc. London432: 171–194.
22.
KumarRSarathiP (2006) Reflection and refraction of thermoelastic plane waves at an interface between two thermoelastic media without energy dissipation. Arch. Mech58: 155–185.
23.
KumarRSinghM (2009) Effect of rotation and imperfection on reflection and transmission of plane waves in anisotropic generalized thermoelastic media. Journal of Sound and Vibration324: 773–797.
24.
LordHWShulmanY (1967) A generalized dynamical theory of thermoelasticity. Journal of Mech. Phys. Solids15: 299–309.
25.
MarinM (1999) An evolutionary equation in thermoelasticity of dipolar bodies. Journal of Mathematical Physiscs40: 1391–1399.
26.
MarinM (2010a) A partition of energy in thermoelsticity of microstretch bodies. Nonlinear Analysis: RWA11: 2436–2447.
27.
MarinM (2010b) Some estimates on vibrations in thermoelasticity of dipolar bodies. Journal of Vibration and Control16: 33–47.
28.
MarinMAgarwalRPMahmoudSR (2013) Modeling a microstretch thermoelastic body with two temperature. Abstract and Applied Analysis. Epub ahead of print 2013, doi: 10.1155/2013/583464.
29.
MarinMStanG (2013) Weak solutions in elasticity of dipolar bodies with stretch. Carpathian Journal of Mathematics29(1): 33–40.
30.
NayfehANasserSN (1971) Thermoelastic waves in solids with thermal relaxation. Acta Mech12: 53–69.
31.
OthmanMIASongY (2007) Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation. International Journal of Solids and Structures44: 5651–5664.
32.
OthmanMIASongY (2008) Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli. Applied Mathematical Modelling32: 483–500.
33.
PangYWangYue-ShengLiuJin-XiFangDai-Ning (2008) Reflection and refraction of plane waves at the interface between piezoelectric and piezomagnetic media. International Journal of Engineering Science46: 1098–1110.
34.
SharmaJN (1988) Reflection of thermoelastic waves from the stress-free insulated boundary of an anisotropic half-space. Indian J Pure Appl Math19: 294–304.
35.
SharmaKMarinM (2014) Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids. Ann Sci22(2): 151–175.
36.
SinghB (2005) Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion. J Earth Syst Sci114: 1–10.
37.
SinghB (2008) Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space. Applied Mathematics and Computation198: 494–505.
38.
SinghBKumarR (1998) Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space. International Journal of Engineering Science36: 865–890.
39.
SinghBKumarR (2003) Wave propagation in a generalized thermo-microstretch elastic solid. International Journal of Engineering Science36: 891–912.
40.
SinhaSBElasibaiKA (1995) Reflection and Refraction of thermoelastic waves at an interface of two semi-infinite media with two relaxation times. J. Thermal Stresses20: 129–145.
41.
SinhaSBElasibaiKA (1996) Reflection of thermoelastic waves at a solid half-space with two relaxation times. J. Thermal Stresses19: 749–762.
42.
SinhaANSinhaSB (1974) Reflection of thermoelastic waves at a solid half-space with thermal relaxation. J. Phys. Earth22: 237–244.
43.
SinghMCChakrabortyN (2013) Reflection and refraction of p-, SV- and thermal waves, at an initial stressed solid-liquid interface in generalized thermoelasticity. Applied Mathematical Modelling37: 463–475.
