Variational Principle and Plane Wave Propagation in Thermoelastic Medium with Double Porosity Under Lord-Shulman Theory
محورهای موضوعی : Engineering
R Kumar
1
(Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India)
R Vohra
2
(Department of Mathematics& Statistics, H.P.University, Shimla, HP, India)
M.G Gorla
3
(Department of Mathematics& Statistics, H.P.University, Shimla, HP, India)
کلید واژه: Phase velocity, Plane waves, Variational principle, Double porosity, Lord-shulman theory, Attenuation quality factor,
چکیده مقاله :
The present study is concerned with the variational principle and plane wave propagation in double porous thermoelastic infinite medium. Lord-Shulman theory [2] of thermoelasticity with one relaxation time has been used to investigate the problem. It is found that for two dimensional model, there exists four coupled longitudinal waves namely longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PV1), and longitudinal volume fractional wave corresponding to fissures (PV2), in addition to, a transverse wave (S) which is not affected by the volume fraction fields and thermal properties. The different characteristics of the wave such as phase velocity and attenuation quality factor are computed numerically and depicted graphically. Some special cases are also deduced from the present investigation.
[1] Biot M. A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[2] Lord H., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics of Physics of Solids 15: 299-309.
[3] Hetnarski R. B., Ignaczak J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451-476.
[4] Biot M. A., 1941, General theory of three-dimensional consolidation, Journal of Applied Physics 12: 155-164.
[5] Bowen R.M.,1980, Incompressible porous media models by use of the theory of mixtures, International Journal of Engineering Science 18: 1129-1148.
[6] De Boer R., Ehlers W., 1990, Uplift, friction and capillarity-Three fundamental effects for liquid saturated porous solids, International Journal of Solids and Structures 26: 43-57.
[7] Barenblatt G.I., Zheltov I.P., Kochina I.N., 1960, Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), Journal of Applied Mathematics and Mechanics 24: 1286-1303.
[8] Wilson R. K., Aifantis E. C.,1982, On the theory of consolidation with double porosity, International Journal of Engineering Science 20(9): 1009-1035.
[9] Khaled M.Y., Beskos D. E., Aifantis E. C.,1984, On the theory of consolidation with double porosity-III, International Journal for Numerical and Analytical Methods in Geomechanics 8: 101-123.
[10] Wilson R. K., Aifantis E. C., 1984, A double porosity model for acoustic wave propagation in fractured porous rock, International Journal of Engineering Science 22(8-10): 1209-1227.
[11] Beskos D. E., Aifantis E. C.,1986., On the theory of consolidation with double porosity-II, International Journal of Engineering Science 24(111): 1697-1716.
[12] Khalili N., Valliappan S., 1996, Unified theory of flow and deformation in double porous media, European Journal of Mechanics - A/Solids 15: 321-336.
[13] Aifantis E. C., 1977, Introducing a multi –porous medium, Developments in Mechanics 8: 209-211.
[14] Aifantis E. C.,1979, On the response of fissured rocks, Developments in Mechanics 10: 249-253.
[15] Aifantis E.C., 1980, On the problem of diffusion in solids, Acta Mechanica 37: 265-296.
[16] Aifantis E.C., 1980, The Mechanics of Diffusion in Solids, T.A.M. Report No. 440, Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, Illinois.
[17] Moutsopoulos K. N., Eleftheriadis I. E., Aifantis E. C.,1996, Numerical simulation of transport phenomena by using the double porosity/ diffusivity continuum model, Mechanics Research Communications 23(6): 577-582.
[18] Khalili N., SelvaduraiA. P. S.,2003, A fully coupled constitutive model for thermo-hydro -mechanical analysis in elastic media with double porosity, Geophysical Research Letters 30: 2268-2271.
[19] Pride S. R., Berryman J. G., 2003, Linear dynamics of double–porosity dual-permeability materials-I, Physical Review E 68: 036603.
[20] Straughan B., 2013, Stability and uniqueness in double porosity elasticity, International Journal of Engineering Science 65:1-8.
[21] Svanadze M., 2005, Fundamental solution in the theory of consolidation with double porosity, Journal of the Mechanical Behavior of Biomedical Materials 16: 123-130.
[22] Svanadze M., 2010, Dynamical problems on the theory of elasticity for solids with double porosity, Proceedings in Applied Mathematics and Mechanics 10: 209-310.
[23] Svanadze M., 2012, Plane waves and boundary value problems in the theory of elasticity for solids with double porosity, Acta Applicandae Mathematicae 122: 461-470.
[24] Svanadze M., 2014, On the theory of viscoelasticity for materials with double porosity, Discrete and Continuous Dynamical Systems - Series B 19(7): 2335-2352.
[25] Svanadze M., 2014, Uniqueness theorems in the theory of thermoelasticity for solids with double porosity, Meccanica 49: 2099-2108.
[26] Scarpetta E., Svanadze M., Zampoli V., 2014, Fundamental solutions in the theory of thermoelasticity for solids with double porosity, Journal of Thermal Stresses 37(6): 727-748.
[27] Scarpetta E., Svanadze M., 2015 ,Uniqueness theorems in the quasi-static theory of thermo elasticity for solids with double porosity, Journal of Elasticity 120: 67-86.
[28] Kumar R., Kansal T., 2014, Propagation of plane waves and fundamental solution in the theories of thermoelastic diffusive materials with voids, International Journal of Applied Mathematics and Mechanics 8(13): 84-103.
[29] Kumar R., Singh M., 2007, Propagation of plane waves in thermoelastic cubic crystal material with two relaxation times, Applied Mathematics and Mechanics 28(5): 627-641.
[30] Kumar R., Kumar R., 2010, Propagation of wave at the boundary surface of transversely isotropic thermoelastic material with voids and isotropic elastic half-space, Applied Mathematics and Mechanics 31(9): 1153-1172.
[31] Kumar R., Kaur M., Rajvanshi S.C., 2014, Plane wave propagation in microstretch thermoelastic medium with microtemperatures, Journal of Vibration and Control 21: 2678.
[32] Iesan D., Quintanilla R, 2014, On a theory of thermoelastic materials with a double porosity structure, Journal of Thermal Stresses 37: 1017-1036.
[33] Sherief H., Saleh H., 2005, A half space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 42: 4484-4493.
[34] Khalili N., 2003, Coupling effects in double porosity media with deformable matrix, Geophysical Research Letters 30(22): 2153.
