Complementary (homogeneous) transient solutions for orthotropic thermoelasticity with thermal relaxation admit plane waves that propagate in a principal plane without spatial attenuation, but with exponential decay in their wake. Three speeds that vary with decay coefficient and propagation direction exist, and each speed is associated with three reflections from a plane surface aligned with another principal plane. As examples, values from both speed sets are presented, as well as angles of reflection and decay coefficients for given incident waves. For a half-space surface that is traction-free but exhibits convection, surface temperature change is derived, and values also presented.

Issue Section:
Research Papers
Keywords:
orthotropy, coupled thermoelasticity, thermal relaxation, plane waves, reflection, wave speeds, dispersion, exponential decay
Topics:
Reflection, Thermoelasticity, Waves, Relaxation (Physics), Transients (Dynamics)

References

1.
Ignaczak
,
J.
, and
Ostoja-Starzewski
,
M.
, 2010,
Thermoelasticity With Finite Wave Speeds
,
Oxford Science
,
New York
.
2.
Brock
,
L. M.
, 2009, “
Basic Problems of Coupled Thermoelasticity With Thermal Relaxation and Pre-Stress: Aspects Observed in Exact and Asymptotic Solutions
,”
J. Therm. Stresses
,
32
, pp.
593
–
622
.
Crossref
Search ADS
 
3.
Brock
,
L. M.
, 2010, “
Reflection and Diffraction of Plane Temperature-Step Waves in Orthotropic Thermoelastic Solids
,”
J. Therm. Stresses
,
33
, pp.
879
–
904
.
Crossref
Search ADS
 
4.
Lindsay
,
R. B.
, 1960,
Mechanical Radiation
,
McGraw-Hill
,
New York
.
5.
Lekhnitskii
,
S. G.
, 1963,
Theory of Elasticity of an Anisotropic Elastic Body
,
Holden-Day
,
San Francisco
.
6.
Ting
,
T. C. T.
, 1996,
Anisotropic Elasticity: Theory and Applications
,
Oxford Science
,
New York
.
7.
Theocaris
,
P. S.
, and
Sokolis
,
D. P.
, 2000, “
Invariant Elastic Constants and Eigentensors of Orthorhombic, Tetragonal, Hexagonal and Cubic Crystalline Media
,”
Acta Crystallogr.
,
56
, pp.
310
–
331
.
8.
Jones
,
R. M.
, 1999,
Mechanics of Composite Materials
, 2nd ed.,
Brunner-Routledge
,
New York
.
9.
Achenbach
,
J. D.
, 1973,
Wave Propagation in Elastic Solids
,
North-Holland
,
Amsterdam
.
10.
Miklowitz
,
J.
, 1978,
The Theory of Elastic Waves and Waveguides
,
North-Holland
,
Amsterdam
.
11.
Lord
,
H. W.
, and
Shulman
,
Y.
, 1967, “
Generalized Dynamical Theory of Thermoelasticity
,”
15
, pp.
297
–
309
.
12.
Payton
,
R. G.
, 1983,
Elastic Wave Propagation in Transversely Isotropic Media
,
Martinus Nijhoff
,
The Hague
.
13.
Chadwick
,
P.
, 1960, “
Thermoelasticity. The Dynamical Theory
,”
Progress in Solid Mechanics
, Vol.
1
,
I. N.
Sneddon
 and
R.
Hill
, eds.,
North-Holland
,
Amsterdam
, pp.
265
–
330
.
14.
Kunz
,
K. S.
, 1957,
Numerical Analysis
,
McGraw-Hill
,
New York
.
15.
Abramowitz
,
M. A.
, and
Stegun
,
I. A.
, 1972,
Handbook of Mathematical Functions
,
Dover
,
New York
.
16.
Sokolnikoff
,
I. S.
, 1956,
Mathematical Theory of Elasticity
,
McGraw-Hill
,
New York
.
17.
Boley
,
B. A.
, and
Weiner
,
J. H.
, 1985,
Theory of Thermal Stresses
,
Krieger
,
Malabar, FL
.
18.
Freund
,
L. B.
, 1993,
Dynamic Fracture Mechanics
,
Cambridge University Press
,
Cambridge
.
19.
Cagniard
,
L.
, 1962,
The Reflection and Refraction of Progressive Seismic Waves
,
E. A.
Flinn
 and
C. H.
Dix
, trans.,
McGraw-Hill
,
New York
.
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 by American Society of Mechanical Engineers
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