Propagation of Wave at the Boundary Surface of Transversely Isotropic Thermoelastic Material With Voids and Isotropic Elastic Half-Space

Rajneesh Kumar; Rajeev Kumar

doi:10.3879/j.issn.1000-0887.2010.09.010

Volume 31 Issue 9

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2010 > 31(9): 1101-1117

Rajneesh Kumar, Rajeev Kumar. Propagation of Wave at the Boundary Surface of Transversely Isotropic Thermoelastic Material With Voids and Isotropic Elastic Half-Space[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1101-1117. doi: 10.3879/j.issn.1000-0887.2010.09.010

Citation:

PDF( 1280 KB)

Propagation of Wave at the Boundary Surface of Transversely Isotropic Thermoelastic Material With Voids and Isotropic Elastic Half-Space

doi: 10.3879/j.issn.1000-0887.2010.09.010

Department of Mathematics, Kurukshetra University, Kurukshetra-136 119, India

Received Date: 1900-01-01
Rev Recd Date: 2010-06-25
Publish Date: 2010-09-15

Abstract

Abstract

The purpose of this research was to study the effect of voids on the surface wave propagation in a layer of transversely isotropic thermoelastic material with voids lying over an isotropic elastic half-space.The frequency equation was derived after developing the mathematical model for welded and smooth contact boundary conditions.The dispersion curves giving the phase velocity and attenuation coefficient verses wave number were plotting graphically to depict the effects of voids and anisotropy for welded contact boundary conditions.The specific loss and amplitudes of volume fraction field,normal stress,temperature change for welded contact are obtained and shown graphically for a particular model to depict the voids and anisotropy effects.Some special cases are also deduced from the present investigation.
- propagation of wave,
- transverse isotropic,
- thermoelastic with voids,
- isotropic elastic half-space,
- phase velocity,
- attenuation coefficient

FullText(HTML)

References(24)

References

[1]	Biot M A. Theory of propagation of elastic waves in a fluid saturated porous solid: I low frequency range[J]. The Journal of the Acoustical Society of America, 1956, 28(2): 168-178. doi: 10.1121/1.1908239
[2]	Biot M A, Willis D G. Elastic coefficients of the theory of consolidation[J].The Journal of the Acoustical Society of America, 1957, 24: 594-601.
[3]	Goodman M A, Cowin S C. A continuum theory of granular material[J]. Archive for Rational Mechanics and Analysis, 1972, 44(4): 249-266.
[4]	Nunziato J W, Cowin S C. A non-linear theory of elastic materials with voids[J]. Archive for Rational Mechanics and Analysis, 1979, 72(2): 175-201.
[5]	Cowin S C, Nunziato J W. Linear elastic materials with voids[J]. Journal of Elasticity, 1983, 13(2): 125-147. doi: 10.1007/BF00041230
[6]	Lord H W, Shulman Y. A generalized dynamical theory of thermoelasticity[J]. Journal of Mechanics and Physics of Solids, 1967, 15(5): 299-309. doi: 10.1016/0022-5096(67)90024-5
[7]	Green A E, Lindsay K A. Thermoelasticity[J]. Journal of Elasticity, 1972, 2: 1-7. doi: 10.1007/BF00045689
[8]	Dhaliwal R S, Sherief H. Generalized thermoelasticity for anisotropic media[J]. Quarterly of Applied Mathematics, 1980, 33: 1-8. doi: 10.1093/qjmam/33.1.1
[9]	Iesan D. A theory of thermoelastic material with voids[J]. Acta Mechanica, 1986, 60(1/2): 67-89. doi: 10.1007/BF01302942
[10]	Iesan D. A theory of initially stressed thermoelastic material with voids[J]. An Stiint Univ Ai I Cuza Iasi Sect I a Mat, 1987, 33: 167-184.
[11]	Dhaliwal R S, Wang J. A heat-flux dependent theory of thermoelasticity with voids[J]. Acta Mech, 1995, 110(1/4): 33-39. doi: 10.1007/BF01215413
[12]	Chirita S, Scalia A. On the spatial and temporal behaviour in linear thermoelasticity of materials with voids[J]. J Thermal Stresses, 2001, 24(5): 433-455. doi: 10.1080/01495730151126096
[13]	Pompei A, Scalia A. On the asymptotic spatial behaviour in linear thermoelasticity of materials with voids[J]. J Thermal Stresses, 2002, 25(2): 183-193. doi: 10.1080/014957302753384414
[14]	Scalia A, Pompei A, Chirita S. On the behaviour of steady time harmonic oscillations thermoelastic materials with voids[J]. J Thermal Stresses, 2004, 27(3):209-226. doi: 10.1080/01495730490264330
[15]	Singh J, Tomer S K. Plane waves in thermoelastic materials with voids[J]. Mech Mat, 2007, 39(10): 932-940. doi: 10.1016/j.mechmat.2007.03.007
[16]	Singh B. Wave propagation in a generalized thermoelastic materials with voids[J]. Appl Math Comput, 2007, 189(1): 698-709. doi: 10.1016/j.amc.2006.11.123
[17]	Ciarletta M, Straughan B. Thermo-poroelastic acceleration waves in elastic materials with voids[J]. J Math Anal Appl, 2007, 333: 142-150. doi: 10.1016/j.jmaa.2006.09.014
[18]	Ciarletta M, Scalia A. On uniqueness and reciprocity in linear thermoelasticity of material with voids[J]. Journal of Elasticity, 1993, 32(1):1-17. doi: 10.1007/BF00042245
[19]	Magana A, Quintanilla R. On the exponential decay of solutions in one-dimensional generalized porous-thermo-elasticity[J]. Asymptotic Analysis, 2006, 49(3/4): 173-187.
[20]	Sturnin D V. On characteristics times in generalized thermoelasticity[J]. J Appl Math, 2001, 68(5): 816-817.
[21]	Kolsky H. Stress Waves in Solids[M]. Oxford: Clarendon Press, 1935.
[22]	Kumar R, Kumar R. Propagation of waves in a layer of transversely isotropic elastic material with voids and rotation overlaying an isotropic elastic half-space[J]. Special Topics and Reviews in Porous Media-An International Journal, 2010, 1(2):145-164. doi: 10.1615/SpecialTopicsRevPorousMedia.v1.i2.50
[23]	Dhaliwal R S, Singh A. Dynamic Coupled Thermoelasticity[M]. Delhi: Hindustan Publishing Corporation, 1980.
[24]	Bullen K E. An Introduction to the Theory of Seismology[M]. Cambridge: Cambridge University Press, 1963.