0
Technical Briefs

Analytical Solution of Coupled Thermoelastic Axisymmetric Transient Waves in a Transversely Isotropic Half-Space

[+] Author and Article Information
M. Raoofian Naeeni

Department of Surveying and Geomatics Engineering,
Center of Excellence in Geomatics,
Engineering and Disaster Prevention,
College of Engineering,
University of Tehran,
11155-4563 Tehran, Iran

M. Eskandari-Ghadi

Associate Professor
School of Civil Engineering,
College of Engineering,
University of Tehran,
11155-4563 Tehran, Iran

Alireza A. Ardalan

Professor
Department of Surveying and Geomatics Engineering,
Center of Excellence in Geomatics,
Engineering and Disaster Prevention,
College of Engineering,
University of Tehran,
11155-4563 Tehran, Iran

M. Rahimian

Professor

Y. Hayati

School of Civil Engineering,
College of Engineering,
University of Tehran,
11155-4563 Tehran, Iran

Manuscript received December 23, 2011; final manuscript received October 1, 2012; accepted manuscript posted October 8, 2012; published online January 25, 2013. Assoc. Editor: Martin Ostoja-Starzewski.

J. Appl. Mech 80(2), 024502 (Jan 25, 2013) (7 pages) Paper No: JAM-11-1492; doi: 10.1115/1.4007786 History: Received December 23, 2011; Revised October 01, 2012; Accepted October 08, 2012

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Jeffreys, H., 1930, “The Thermodynamics of an Elastic Solid,” Proc. Cambridge Philos. Soc., 26, pp. 101–106. [CrossRef]
Nowacki, W., 1962, Thermoelasticity, Addison-Wesley, Reading MA.
Biot, M. A., 1956, “Thermoelasticity and Irreversible Thermodynamics,” J. Appl. Phys., 27(3), pp. 240–253. [CrossRef]
MacDowell, E. L., and Sternberg, E., 1957, “On the Steady State Thermoelastic Problem for Half-Space,” Q. Appl. Math., 14, pp. 381–398.
Virruijt, A., 1967, “The Completeness of Biot's Solution of the Coupled Thermoelastic Problem,” Q. Appl. Math., 26(4), pp. 485–490.
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.
Zorski, H., 1958, “Singular Solutions for Thermoelastic Media,” Bull. Acad. Pol. Sci., Ser. Sci. Tech., 6, pp. 331–339.
Sharma, B., 1958, “Thermal Stresses in Transversely Isotropic Semi-Infinite Elastic Solids,” J. Appl. Mech., 25, pp. 86–88.
Singh, A., 1960, “Axisymmetrical Thermal Stresses in Transversely Isotropic Bodies,” Arch. Mech. Stosow., 12(3), pp. 287–394.
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. [CrossRef]
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. [CrossRef]
Eskandari-Ghadi, M., Rahimian, M., Sture, S., and Forati, M., 2012, “Thermoelastodynamics in Transversely Isotropic Media With Scalar Potential Functions,” J. Appl. Mech., (submitted).
Haojiang, D., Fenglin, G., and Pengfei, H., 2000, “General Solutions of Coupled Thermoelastic Problems,” J. Appl. Math. Mech., 21(6), pp. 631–636. [CrossRef]
Carlson, D., 1972, “Linear Thermoelasticity,” Encyclopedia of Physics, Vol. VI a/2, S.Flügge, ed., Springer-Verlag, Berlin, pp. 297–345.
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.
Lekhnitskii, S. G., 1981, Theory of Elasticity of an Anisotropic Body, Dover Publications Inc., Mineola, NY.
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.
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. [CrossRef]
Mallet, A., 1985, “Numerical Inversion of Laplace Transform,” http://library.wolfram.com/infocenter/MathSource/2691/
Abate, J., and Valko, P. P., 2004, “Multi-Precision Laplace Transform Inversion,” Int. J. Numer. Methods Eng., 60, pp. 979–993. [CrossRef]
Sidi, A., 1982, “The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation,” Math. Comput., 38(158), pp. 517–529. [CrossRef]
Longman, I. M., 1956, “Note on a Method for Computing Infinite Integrals of Oscillatory Functions,” Proc. Cambridge Philos. Soc., 52(4), pp. 764–768. [CrossRef]
Levin, D., 1977, “Analysis of Collocation Method for Integrating Rapidly Oscillatory Functions,” J. Comput. Appl. Math., 78, pp. 131–138. [CrossRef]
Levin, D., 1977, “Fast Integration of Rapidly Oscillatory Function,” J. Comput. Appl. Math., 67, pp. 95–101. [CrossRef]
Pekeris, C. L., 1965a, “The Seismic Surface Pulse,” Proc. Natl. Acad. Sci. U.S.A., 41, pp. 629–639. [CrossRef]
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.
Eskandari Ghadi, M., and Sattar, S., 2009, “Axisymmetric Transient Waves in Transversely Isotropic Half-Space,” Soil Dyn. Earthquake Eng., 29, pp. 347–355. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Transversely isotropic thermoelastic half-space under arbitrary surface tractions and flux

Grahic Jump Location
Fig. 2

Surface radial displacement of an elastic Poisson material (material 1) subjected to a point force varying with time as a Heaviside step function

Grahic Jump Location
Fig. 3

Surface vertical displacement of an elastic Poisson material (material 1) subjected to a point force varying with time as a Heaviside step function

Grahic Jump Location
Fig. 4

Normalized surface radial displacement of transversely isotropic thermoelastic material 2 under the application of point force varies with time as a Heaviside step function

Grahic Jump Location
Fig. 5

Normalized surface temperature change of transversely isotropic material 3 under the application of point force varying with time as a Heaviside step function

Grahic Jump Location
Fig. 6

Normalized surface vertical displacement of material 3, under the application of point heat flux varies with time as a Heaviside step function

Grahic Jump Location
Fig. 7

Normalized surface temperature change for transversely isotropic thermoelastic material 3, under the application of point heat source varies with time as a Heaviside step

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In