A half-space containing transversely isotropic thermoelastic material with a depth-wise axis of material symmetry is considered to be under the effects of axisymmetric transient surface thermal and forced excitations. With the use of a new scalar potential function, the coupled equations of motion and energy equation are uncoupled, and the governing equation for the potential function, is solved with the use of Hankel and Laplace integral transforms. As a result, the displacements and temperature are represented in the form of improper double integrals. The solutions are also investigated in detail for surface traction and thermal pulses varying with time as Heaviside step function. It is also shown that the derived solutions degenerate to the results given in the literature for isotropic materials. Some numerical evaluations for displacement and temperature functions for two different transversely isotropic materials with different degree of anisotropy are presented to portray the dependency of response on the thermal properties as well as the degree of anisotropy of the medium.

References

References
1.
Jeffreys
,
H.
,
1930
, “
The Thermodynamics of an Elastic Solid
,”
Proc. Cambridge Philos. Soc.
,
26
, pp.
101
106
.10.1017/S0305004100015085
2.
Nowacki
,
W.
,
1962
,
Thermoelasticity
,
Addison-Wesley
,
Reading MA
.
3.
Biot
,
M. A.
,
1956
, “
Thermoelasticity and Irreversible Thermodynamics
,”
J. Appl. Phys.
,
27
(
3
), pp.
240
253
.10.1063/1.1722351
4.
MacDowell
,
E. L.
, and
Sternberg
,
E.
,
1957
, “
On the Steady State Thermoelastic Problem for Half-Space
,”
Q. Appl. Math.
,
14
, pp.
381
398
.
5.
Virruijt
,
A.
,
1967
, “
The Completeness of Biot's Solution of the Coupled Thermoelastic Problem
,”
Q. Appl. Math.
,
26
(
4
), pp.
485
490
.
6.
Deresiewicz
,
H.
,
1958
, “
Solution of the Equations of Thermoelasticity
,”
Proceedings of the 3rd U.S. National Congress on Applied Mechanics, Brown University
,
Providence, RI
, June 11–14, ASME, New York, pp.
287
291
.
7.
Zorski
,
H.
,
1958
, “
Singular Solutions for Thermoelastic Media
,”
Bull. Acad. Pol. Sci., Ser. Sci. Tech.
,
6
, pp.
331
339
.
8.
Sharma
,
B.
,
1958
, “
Thermal Stresses in Transversely Isotropic Semi-Infinite Elastic Solids
,”
J. Appl. Mech.
,
25
, pp.
86
88
.
9.
Singh
,
A.
,
1960
, “
Axisymmetrical Thermal Stresses in Transversely Isotropic Bodies
,”
Arch. Mech. Stosow.
,
12
(
3
), pp.
287
394
.
10.
Noda
,
N.
,
Takeuti
,
Y.
, and
Sugano
,
Y.
,
1985
, “
On a General Treatise of Three-Dimensional Thermoelastic Problems in Transversely Isotropic Bodies
,”
Z. Angew. Math. Mech.
,
65
(
10
), pp.
509
512
.10.1002/zamm.19850651010
11.
Noda
,
N.
, and
Ashida
,
F.
,
1985
, “
A Three-Dimensional Treatment of Transient Thermal Stresses in Transversely Isotropic Semi-Infinite Circular Cylinder Subjected to an Asymmetric Temperature on the Cylindrical Surface
,”
Acta. Mech.
,
58
, pp.
175
191
.10.1007/BF01176598
12.
Eskandari-Ghadi
,
M.
,
Rahimian
,
M.
,
Sture
,
S.
, and
Forati
,
M.
,
2012
, “
Thermoelastodynamics in Transversely Isotropic Media With Scalar Potential Functions
,”
J. Appl. Mech.
, (submitted).
13.
Haojiang
,
D.
,
Fenglin
,
G.
, and
Pengfei
,
H.
,
2000
, “
General Solutions of Coupled Thermoelastic Problems
,”
J. Appl. Math. Mech.
,
21
(
6
), pp.
631
636
.10.1007/BF02460181
14.
Carlson
,
D.
,
1972
, “
Linear Thermoelasticity
,”
Encyclopedia of Physics
, Vol.
VI a/2
,
S.
Flügge
, ed.,
Springer-Verlag
,
Berlin
, pp.
297
345
.
15.
Eubanks
,
R. A.
, and
Strenberg
,
E.
,
1954
, “
On the Axisymmetric Problem of Elasticity Theory for a Medium With Transverse Isotropy
,”
J. Ration. Mech.
,
3
, pp.
89
101
.
16.
Lekhnitskii
,
S. G.
,
1981
,
Theory of Elasticity of an Anisotropic Body
,
Dover Publications Inc.
,
Mineola, NY
.
17.
Sharma
,
J. N.
, and
Singh
,
H.
,
1984
, “
Thermoelastic Surface Waves in Transversely Isotropic Half-Space With Thermal Relaxations
,”
Indian J. Pure Appl. Math.
,
16
(
10
), pp.
1202
1219
.
18.
Nayfeh
,
A. H.
, and
Nemat-Nasser
,
S.
,
1972
, “
Transient Thermoelastic Waves in Half-Space With Thermal Relaxation
,”
J. Appl. Math. Phys.
,
23
(
1
), pp.
50
68
.10.1007/BF01593202
19.
Mallet
,
A.
,
1985
, “
Numerical Inversion of Laplace Transform
,” http://library.wolfram.com/infocenter/MathSource/2691/
20.
Abate
,
J.
, and
Valko
,
P. P.
,
2004
, “
Multi-Precision Laplace Transform Inversion
,”
Int. J. Numer. Methods Eng.
,
60
, pp.
979
993
.10.1002/nme.995
21.
Sidi
,
A.
,
1982
, “
The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation
,”
Math. Comput.
,
38
(
158
), pp.
517
529
.10.1090/S0025-5718-1982-0645667-5
22.
Longman
,
I. M.
,
1956
, “
Note on a Method for Computing Infinite Integrals of Oscillatory Functions
,”
Proc. Cambridge Philos. Soc.
,
52
(
4
), pp.
764
768
.10.1017/S030500410003187X
23.
Levin
,
D.
,
1977
, “
Analysis of Collocation Method for Integrating Rapidly Oscillatory Functions
,”
J. Comput. Appl. Math.
,
78
, pp.
131
138
.10.1016/S0377-0427(96)00137-9
24.
Levin
,
D.
,
1977
, “
Fast Integration of Rapidly Oscillatory Function
,”
J. Comput. Appl. Math.
,
67
, pp.
95
101
.10.1016/0377-0427(94)00118-9
25.
Pekeris
,
C. L.
,
1965a
, “
The Seismic Surface Pulse
,”
Proc. Natl. Acad. Sci. U.S.A.
,
41
, pp.
629
639
.10.1073/pnas.41.9.629
26.
Das
,
N. C.
, and
Lahiri
,
A.
,
2009
, “
Eigenvalue Approach to Three Dimensional Coupled Thermoelasticity in a Rotating Transversely Isotropic Medium
,”
Tamsui Oxford J. Math. Sci.
,
25
(
3
), pp.
237
257
.
27.
Eskandari Ghadi
,
M.
, and
Sattar
,
S.
,
2009
, “
Axisymmetric Transient Waves in Transversely Isotropic Half-Space
,”
Soil Dyn. Earthquake Eng.
,
29
, pp.
347
355
.10.1016/j.soildyn.2008.01.017
You do not currently have access to this content.