A three-dimensional transient thermoelastic solution is obtained for Rayleigh-type disturbances propagating on the surface of a half-space. These surface waves are generated by either a buried or surface thermal source, which has the form of a concentrated heat flux applied impulsively. In an effort to model this problem as realistically as possible, the half-space material is taken to respond according to Biot’s fully coupled thermoelasticity. The problem has relevance to situations involving heat generation due to: (i) laser action (impulsive electromagnetic radiation) on a surface target, (ii) underground nuclear activity, and (iii) friction developed during underground fault motions related to seismic activity. The problem was attacked with unilateral and double bilateral Laplace transforms, which suppress, respectively, the time variable and two of the space variables. The Rayleigh wave contribution is obtained as a closed-form expression by utilizing asymptotics, complex-variable theory and certain results for Bessel functions. The dependence of the normal displacement associated with the Rayleigh wave upon the distance from the source epicenter and the distance from the wavefront is also determined.
Issue Section:
Technical Papers
1.
Morland
, L. W.
, 1968
, “Generation of Thermoelastic Stress Waves by Impulsive Electromagnetic Radiation
,” AIAA J.
, 6
, pp. 1063
–1070
.2.
Sve
, C.
, and Miklowitz
, J.
, 1973
, “Thermally Induced Stress Waves in an Elastic Layer
,” ASME J. Appl. Mech.
, 40
, pp. 161
–168
.3.
Bechtel
, J. H.
, 1975
, “Heating of Solid Targets With Laser Pulses
,” J. Appl. Phys.
, 46
, pp. 1585
–1593
.4.
Hetnarski
, R. B.
, and Ignaczak
, J.
, 1994
, “Generalized Thermoelasticity: Response of Semi-Space to a Short Laser Pulse
,” J. Therm. Stresses
, 17
, pp. 377
–396
.5.
Royer
, D.
, and Chenu
, C.
, 2000
, “Experimental and Theoretical Waveforms of Rayleigh Waves Generated by a Thermoelastic Laser Line Source
,” Ultrasonics
, 38
, pp. 891
–895
.6.
Bullen, K. E., and Bolt, B. A., 1987, An Introduction to the Theory of Seismology, Cambridge University Press, Cambridge.
7.
Kanamori
, H.
, Anderson
, D. L.
, and Heaton
, T. H.
, 1995
, “Frictional Melting During the Rupture of the 1994 Bolivian Earthquake
,” Science
, 279
, pp. 839
–841
.8.
Biot
, M. A.
, 1956
, “Thermoelasticity and Irreversible Thermodynamics
,” J. Appl. Phys.
, 27
, pp. 240
–253
.9.
Achenbach, J. D., 1973, Wave Propagation in Elastic Solids, North–Holland, NY.
10.
Garvin
, W. W.
, 1956
, “Exact Transient Solution of the Buried Line Source Problem
,” Proc. R. Soc. London, Ser. A
, 234
, pp. 528
–541
.11.
Pekeris
, C. L.
, and Lifson
, H.
, 1957
, “Motion of the Surface of a Uniform Elastic Half-Space Produced by a Buried Pulse
,” J. Acoust. Soc. Am.
, 29
, pp. 1233
–1238
.12.
Lykotrafitis
, G.
, Georgiadis
, H. G.
, and Brock
, L. M.
, 2001
, “Three-Dimensional Thermoelastic Wave Motions in a Half-Space Under the Action of a Buried Source
,” Int. J. Solids Struct.
, 38
, pp. 4857
–4878
.13.
Boley
, B. A.
, and Tolins
, I. S.
, 1962
, “Transient Coupled Thermoelastic Boundary Value Problems in the Half-Space
,” ASME J. Appl. Mech.
, 29
, pp. 637
–646
.14.
Hetnarski
, R. B.
, and Ignaczak
, J.
, 1993
, “Generalized Thermoelasticity: Closed-Form Solutions
,” J. Therm. Stresses
, 16
, pp. 473
–498
.15.
Predeleanu, M., 1987, “Analysis of Thermomechanical Coupling by Boundary Element Method,” in Thermomechanical Couplings in Solids, edited by Bui, H. D. and Nguyen, Q. S., Elsevier, Amsterdam, pp. 305–318.
16.
Fleurier
, J.
, and Predeleanu
, M.
, 1987
, “On the Use of Coupled Fundamental Solutions in B.E.M. for Thermoelastic Problems
,” Eng. Anal. Boundary Elem.
, 4
, pp. 70
–74
.17.
Sharp, S., and Crouch, S. L., 1987, “Heat Conduction, Thermoelasticity and Consolidation,” in Boundary Element Methods in Mechanics, edited by Beskos, D. E., Elsevier, Amsterdam, pp. 440–498.
18.
Manolis
, G. D.
, and Beskos
, D. E.
, 1989
, “Integral Formulation and Fundamental Solutions of Dynamic Poroelasticity and Thermoelasticity
,” Acta Mech.
, 76
, pp. 89
–104
.19.
Manolis
, G. D.
, and Beskos
, D. E.
, 1990
, “Integral Formulation and Fundamental Solutions of Dynamic Poroelasticity and Thermoelasticity
,” Acta Mech.
, 83
, pp. 223
–226
.20.
Hetnarski
, R. B.
, 1961
, “Coupled One-Dimensional Thermal Shock Problem for Small Times
,” Arch. Mech. Stosow.
, 13
, pp. 295
–306
.21.
Sternberg
, E.
, and Chakravorty
, J. G.
, 1959
, “On Inertia Effects in a Transient Thermoelastic Problem
,” ASME J. Appl. Mech.
, 26
, pp. 503
–509
.22.
Sternberg
, E.
, and Chakravorty
, J. G.
, 1959
, “Thermal Shock in an Elastic Body With a Spherical Cavity
,” Q. Appl. Math.
, 17
, pp. 205
–218
.23.
Francis
, P. H.
, 1972
, “Thermo-Mechanical Effects in Elastic Wave Propagation: A Survey
,” J. Sound Vib.
, 21
, pp. 181
–192
.24.
Atkinson
, C.
, and Craster
, R. V.
, 1992
, “Fracture in Fully Coupled Dynamic Thermoelasticity
,” J. Mech. Phys. Solids
, 40
, pp. 1415
–1432
.25.
Brock
, L. M.
, 1995
, “Slip/Diffusion Zone Formation at Rapidly-Loaded Cracks in Thermoelastic Solids
,” J. Elast.
, 40
, pp. 183
–206
.26.
Brock
, L. M.
, Rodgers
, M.
, and Georgiadis
, H. G.
, 1996
, “Dynamic Thermoelastic Effects for Half-Planes and Half-Spaces With Nearly-Planar Surfaces
,” J. Elast.
, 44
, pp. 229
–254
.27.
Brock
, L. M.
, Georgiadis
, H. G.
, and Tsamasphyros
, G.
, 1997
, “The Coupled Thermoelasticity Problem of the Transient Motion of a Line Heat/Mechanical Source Over a Half-Space
,” J. Therm. Stresses
, 20
, pp. 773
–795
.28.
Georgiadis
, H. G.
, Brock
, L. M.
, and Rigatos
, A. P.
, 1998
, “Transient Concentrated Thermal/Mechanical Loading of the Faces of a Crack in a Coupled-Thermoelastic Solid
,” Int. J. Solids Struct.
, 35
, pp. 1075
–1097
.29.
Georgiadis
, H. G.
, Rigatos
, A. P.
, and Brock
, L. M.
, 1999
, “Thermoelastodynamic Disturbances in a Half-Space Under the Action of a Buried Thermal/Mechanical Line Source
,” Int. J. Solids Struct.
, 36
, pp. 3639
–3660
.30.
Barber
, J. R.
, 1972
, “Distortion of the Semi-Infinite Solid Due to Transient Surface Heating
,” Int. J. Mech. Sci.
, 14
, pp. 377
–393
.31.
Barber
, J. R.
, and Martin-Moran
, C. J.
, 1982
, “Green’s Functions for Transient Thermoelastic Contact Problems for the Half-Plane
,” Wear
, 79
, pp. 11
–19
.32.
Chadwick, P., 1960, “Thermoelasticity: The Dynamical Theory,” in Progress in Solid Mechanics, edited by Sneddon, I. N. and Hill, R., North–Holland, Amsterdam, Vol. 1, pp. 263–328.
33.
Carlson, D. E., 1972, “Linear Thermoelasticity,” in Handbuch der Physik, edited by Flugge, S., Springer-Verlag, Berlin, VIa/2, pp. 297–345.
34.
Ignaczak
, J.
, and Nowacki
, W.
, 1962
, “The Sommerfeld Radiation Conditions for Coupled Problems of Thermoelasticity
,” Arch. Mech. Stosow.
, 1
, pp. 3
–13
.35.
Pekeris
, C. L.
, 1955
, “The Seismic Buried Pulse
,” Proc. Natl. Acad. Sci. U.S.A.
, 41
, pp. 629
–638
.36.
Miklowitz, J., 1978, The Theory of Elastic Waves and Waveguides, North–Holland, Amsterdam.
37.
van der Pol, B., and Bremmer, H., 1950, Operational Calculus Based on the Two-Sided Laplace Integral, Cambridge University Press, Cambridge.
38.
Carrier, G. F., Krook, M., and Pearson, C. E., 1966, Functions of a Complex Variable, McGraw–Hill, New York.
39.
deHoop
, A. T.
, 1960
, “The Surface Line Source Problem
,” Appl. Sci. Res., Sect. B
, 8
, pp. 349
–356
.40.
Garvin
, W. W.
, 1965
, “Exact Transient Solution of the Buried Line Source Problem
,” Proc. R. Soc. London, Ser. A
, 234
, pp. 528
–541
.41.
Payton
, R. G.
, 1968
, “Epicenter Motion of an Elastic Half-Space Due to Buried Stationary and Moving Line Sources
,” Int. J. Solids Struct.
, 4
, pp. 287
–300
.42.
Viktorov, I. A., 1967, Rayleigh and Lamb Waves, Plenum Press, NY.
43.
Ablowitz, M. J., and Fokas, A. S., 1997, Complex Variables, Cambridge University Press, Cambridge.
44.
Watson, G. N., 1966, Theory of Bessel Functions, Cambridge University Press, Cambridge.
45.
Bracewell, R., 1965, The Fourier Transform and Its Applications, McGraw–Hill, New York.
46.
Markenscoff
, X.
, and Ni
, L.
, 2001
, “The Transient Motion of a Dislocation With a Ramp-Like Core
,” J. Mech. Phys. Solids
, 49
, pp. 1603
–1619
.47.
Chao
, C. C.
, Bleich
, H. H.
, and Sackman
, J.
, 1961
, “Surface Waves in an Elastic Half Space
,” ASME J. Appl. Mech.
, 28
, pp. 300
–301
.Copyright © 2005
by ASME
You do not currently have access to this content.
