A spectral study is performed to gain insight into the effects of relaxation times and thermomechanical coupling on dynamic thermoe Iastic responses in generalized thermoelasticity. The hyperbolic thermoelastic theories of Lord and Schulman (LS) and Green and Lindsay (GL) are selected for the study. A generalized characteristic equation is derived to investigate dispersion behavior of thermoelastic waves as functions of thermomechanical coupling and relaxation time constants. Thermomechanical coupling is found to impose a significant influence on phase velocities. The GL model implicitly indicates that the order of magnitude of the thermomechanical relaxation time can never be greater than that of thermal relaxation time.

Issue Section:
Technical Papers
Topics:
Relaxation (Physics), Thermoelasticity, Thermomechanics, Waves
1.
Achenbach, J. D., 1973, Wave Propagation in Elastic Solids, American Elsevier, New York.
2.
Chandrasekharaiah
D. S.
,
1986
, “
Thermoelasticity With Second Sound: A Review
,”
ASME Appl. Mech. Review
, Vol.
39
, pp.
355
–
376
.
3.
Chen
T.-C.
, and
Weng
C.-I.
,
1988
, “
Generalized Coupled Transient Thermoelastic Plane Problems by Laplace Transform/Finite Element Method
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
55
, pp.
377
–
382
.
4.
Doyle
J. F.
,
1988
, “
Spectral Analysis of Coupled Thermoelastic Waves
,”
Journal Therm. Stresses
, Vol.
11
, pp.
175
–
185
.
5.
Green
A. E.
, and
Lindsay
K. E.
,
1972
, “
Thermoelasticity
,”
Journal Elasticity
, Vol.
2
, pp.
1
–
7
.
6.
Hetnarski
R. B.
, and
Ignaczak
J.
,
1993
, “
Generalized Thermoelasticity: Closed Form Solutions
,”
Journal Them. Stresses
, Vol.
16
, pp.
473
–
498
.
7.
Hetnarski
R. B.
, and
Ignaczak
J.
,
1994
, “
Generalized Thermoelasticity: Response of Semi-Space to a Short Laser Pulse
,”
Journal Therm. Stresses
, Vol.
17
, pp.
377
–
396
.
8.
Ignaczak
J.
,
1980
, “
Linear Dynamic Thermoelasticity—A Survey
,”
Shock Vib. Dig.
, Vol.
13
, pp.
3
–
8
.
9.
Jakubowska
M.
,
1984
, “
Kirhchoff’s Type Formula in Thermoelasticity with Finite Wave Speeds
,”
Journal Therm. Stresses
, Vol.
7
, pp.
259
–
288
.
10.
Lord
H. W.
, and
Schulman
Y.
,
1967
, “
A Generalized Dynamic Theory of Thermoelasticity
,”
Journal Mech. Phys. Solids
, Vol.
15
, pp.
299
–
309
.
11.
Nowinski, J. L., 1978, Theory of Thermoelasticity with Applications, Sijthoff & Noordhoff International Publishers, Alpen aan den Rijn, The Netherlands.
12.
Sanderson
T.
,
Ume
C.
, and
Jarzynski
J.
,
1995
, “
Hyperbolic Heat Equations in Laser Generated Ultrasound Models
,”
Ultrasonics
, Vol.
33
, No.
6
, pp.
415
–
421
.
13.
Spicer, J. B., 1991, “Laser Ultrasonics in Finite Structures: Comprehensive Modeling with Supporting Experiment,” Ph.D. dissertation, Johns Hopkins University, Baltimore, MD.
14.
Tao
D.
, and
Provost
J. H.
,
1984
, “
Relaxation Effects on Generalized Thermo-elasticity Wave
,”
Journal Therm. Stresses
, Vol.
7
, pp.
79
–
89
.
15.
Wegner
J. L.
, and
Haddow
J. B.
,
1993
, “
Linear Thermoelasticity, Second Sound and The Entropy Inequality
,”
Wave Motions
, Vol.
18
, pp.
67
–
77
.
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