The present paper is concerned with the propagation of shear waves in an anisotropic inhomogeneous layer whose elastic constants are functions of temperature. The dependence of material properties on temperature gives rise to inhomogeneity of the layer which is one of the trivial characteristics of the constituent layers of earth which may cause due to the presence of various types of elements and compounds beneath the earth. The layer is lying over a rigid foundation and there is no loading on the upper boundary. The dispersion equation of shear waves has been obtained in closed form. Numerical computations are performed and graphs are plotted to show the effect of inhomogeneity and anisotropy factors on the dimensionless phase velocity. It is found that the phase velocity is considerably influenced by the inhomogeneity and anisotropy of the layer.

1.
J.
 
Nowiński
,
Thermoelastic problem for an isotropic sphere with temperature dependent properties
,
Z Angew Math Phys
,
10
,
565
–
575
(
1959
).
https://doi.org/10.1007/BF01601612
Google Scholar
Crossref
Search ADS
 
2.
J.
 
Nowiński
,
A Betti–Rayleigh theorem for elastic bodies exhibiting temperature dependent properties
,
Appl Sci Res
,
A9
,
429
–
436
(
1960
).
https://doi.org/10.1007/BF00382220
Google Scholar
Crossref
Search ADS
 
3.
J.
 
Nowiński
,
Transient thermoelastic problems for an infinite medium with a spherical cavity exhibiting temperature dependent properties
.
J Appl Mech
,
29
,
399
–
407
(
1962
).
https://doi.org/10.1115/1.3640561
Google Scholar
Crossref
Search ADS
 
4.
J. L.
 
Nowiński
,
Theory of Thermoelasticity with Applications
.
Alphen aan den Rijn, Sijthoff and Noordhoff
,
1978
.
Google Scholar
Crossref
Search ADS
 
5.
L. N.
 
Tao
,
The heat conduction problem with temperature-dependent material properties
,
Int J Heat Mass Tran
,
32
,
487
–
491
(
1989
).
https://doi.org/10.1016/0017-9310(89)90136-1
Google Scholar
Crossref
Search ADS
 
6.
H. J.
 
Lee
, and
D. A.
 
Saravanos
,
The effect of temperature dependent material properties on the response of piezoelectric composite materials
,
J Intel Mater Syst Struct
,
9
,
503
–
508
(
1998
).
https://doi.org/10.1177/1045389X9800900702
Google Scholar
Crossref
Search ADS
 
7.
D. A.
 
Czaplewski
,
J. P.
 
Sullivan
,
T. A.
 
Friedmann
 et al,
Temperature dependence of the mechanical properties of tetrahedrally coordinated amorphous carbon thin films
,
Appl Phys Lett
,
87
,
161,915
–
161,918
(
2005
).
https://doi.org/10.1063/1.2108132
Google Scholar
Crossref
Search ADS
 
8.
A. R.
 
Tillmann
,
V. L.
 
Borges
,
G.
 
Guimaraes
, et al,
Identification of temperature-dependent thermal properties of solid materials
,
J Brazil Soc Mech Sci Eng
,
30
,
269
–
278
(
2008
).
https://doi.org/10.1590/S1678-58782008000400001
Google Scholar
Crossref
Search ADS
 
9.
E.
 
Schreiber
,
O. L.
 
Anderson
 and
N.
 
Soga
,
Elastic Constants and Their Measurement
.
Mc Graw-Hill
,
1973
.
Google Scholar
 
10.
T.
 
Hata
,
Thermoelastic problem for a Griffith crack in a plate with temperature-dependent properties under a linear temperature distribution
,
J Therm Stresses
,
2
,
353
–
366
(
1979
).
https://doi.org/10.1080/01495737908962412
Google Scholar
Crossref
Search ADS
 
11.
T.
 
Hata
,
Thermoelastic problem for a Griffith crack in a plate whose shear modulus is an exponential function of the temperature
,
Z Angew Math Mech
,
61
,
81
–
87
(
1981
).
https://doi.org/10.1002/zamm.19810610204
Google Scholar
Crossref
Search ADS
 
12.
H.
 
Kern
, P-and S-wave velocities in crustal and mantle rocks under the simultaneous action of high confining pressure and high temperature and the effect of the rock microstructure. In:
Schreyer
 
W
, editor.
High Pressure Res Geosci
 
Stuttgart
:
E. Schreizerbart’tsche Verlagsbuchhandlung
,
15
–
45
(
1982
).
Google Scholar
 
13.
R. D.
 
Dwivedi
,
R. K.
 
Goel
,
V. V. R.
 
Prasad
 et al 
Thermo-mechanical properties of Indian and other granites
,
Int J Rock Mech Min Sci
,
45
,
303
–
315
(
2008
).
https://doi.org/10.1016/j.ijrmms.2007.05.008
Google Scholar
Crossref
Search ADS
 
14.
S. J.
 
Matysiak
,
Wave fronts in elastic media with temperature dependent properties
,
Appl Sci Res
,
45
,
97
–
106
(
1988
).
https://doi.org/10.1007/BF00386206
Google Scholar
Crossref
Search ADS
 
15.
M.
 
Aouadi
 and
A. S.
 
El-Karamany
,
Plane waves in generalized thermoviscoelastic material with relaxation time and temperature-dependent properties
,
J Therm Stresses
,
26
,
197
–
222
(
2003
).
https://doi.org/10.1080/713855894
Google Scholar
Crossref
Search ADS
 
16.
K.
 
Kimoto
 and
S.
 
Hirose
,
A Green’s Function Boundary Element Method for SH-Wave Scattering in an Elastic Layer
,
AIP Conf. Proc.
,
700
,
118
–
125
(
2004
).
https://doi.org/10.1063/1.1711614
Google Scholar
Crossref
Search ADS
 
17.
P. C.
 
Pal
,
B.
 
Prasad
 and
S.
 
Kumar
,
Reflection and transmission of SH-waves through a self-reinforced elastic layer embedded between two transversely isotropic inhomogeneous elastic half-spaces
.
Journal of the Geological Society of India 2016
; DOI:
https://doi.org/10.17491/cgsi/2016/95896
.
18.
C.
 
Smerzini
,
J.
 
Avilés
,
F. J.
 
Sánchez-Sesma
 and
R.
 
Paolucci
,
Analytical solutions for the seismic response of underground structures under SH wave propagation
,
AIP Conf. Proc.
 
1020
,
674
–
683
(
2008
).
https://doi.org/10.1063/1.2963900
Google Scholar
Crossref
Search ADS
 
19.
S.
 
Mukhopadhyay
 and
R
,
Kumar
,
Solution of a problem of generalized thermoelasticity of an annular cylinder with variable material properties by finite difference method
,
Comput Meth Sci Tech
,
15
,
169
–
176
(
2009
).
https://doi.org/10.12921/cmst.2009.15.02.169-176
Google Scholar
Crossref
Search ADS
 
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