Wave Propagation in Micropolar Thermoelastic Diffusion Medium

Subject Areas : Engineering

A Miglani ¹ , S Kaushal ²

1 - Department of Mathematics, C.D.L.University, Sirsa-Haryana ,India
2 - Department of Mathematics, Maharishi Markandeshwar University, Mullana-Ambala (Haryana),

Received: 2012-06-04 Accepted : 2012-07-05 Published : 2012-06-30

Keywords: Amplitude ratios, Micropolar, Reflection, Diffusion, Free plane,

Abstract :

The present investigation is concerned with the reflection of plane waves from a free surface of a micropolar thermoelastic diffusion half space in the context of coupled theory of thermoelastic diffusion. The amplitude ratios of various reflected waves are obtained in a closed form. The dependence of these amplitude ratios with an angle of propagation as well as other material parameter are shown graphically. Effects of micropolarity and diffusion are observed on these amplitude ratios. Some special cases of interest are also deduced from the present investigation.

References:

[1] Eringen A.C., 1968, Theory of Micropolar Elasticity, In Fractuce,ed H.Lieboneitz Vol-5. Acamdemic press, Newyork.

[2] Eringen A.C., 1999, Micro Continum Field Theories-I, Foundation and Solids, Springer- Verlag, Berlin.

[3] Nowacki W., 1986, Theory of Asymmetric Elasticity, Pergamon, Oxford.

[4] Touchert T. R., Claus W.D., Jr and Ariman T., 1968, The linear theory of micropolar thermoelasticity, International Journal of Engineering Science 6:37-47.

[5] Nowacki W., 1974, Dynamical problems of thermo diffusion in solids-I, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Techniques 22: 55-64.

[6] Nowacki W., 1974, Dynamical problems of thermo diffusion in solids II, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Techniques 22:129-135.

[7] Nowacki W., 1974, Dynamical problems of thermo diffusion in solids III, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Techniques 22: 257-266.

[8] Nowacki W., 1976, Dynamical problems of thermo diffusion in solids, Engineering Fracture Mechanics8: 261-266.

[9] Sherief H.H., Saleh H., Hamza F., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42:591-608.

[10] Singh B., 2005, Reflection of P and SV waves from free surface of an elastic soild with generalized thermodiffusion, Journal of Earth Sciences 114 (2): 159-168.

[11] Singh B., 2006, Reflection of SV waves from free surface of an elastic soild with generalized thermoelastic diffusion, Journal of Sound and Vibration 291(3-5):764-778.

[12] Aouadi M., 2007, Uniqueness and recipocity theorem in the theory of generalized thermoelasic diffusion, Journal of Thermal streses 30:665-678.

[13] Aouadi M., 2008, Generalized theory of thermoelasic diffusion for an anisotropic media, Journal of Thermal streses 31:270-285.

[14] Sharma N., Kumar R., Ram P., 2008, Plane strain deformation in generalized thermoelastic diffusion, International Journal of Thermophysics 29: 1503-1522.

[15] Sherief H.H., El-Maghraby N.M., 2009, A thick plate problem in the theory of generalized thermoelastic diffusion, International Journal of Thermophysics 30:2044-2057.

[16] Othman M.I.A., Farouk R. M., Hamied H., A. El., 2009, The dependence of the modulus of elasticity on reference temperature in the theory of generalized thermoelastic diffusion with one relaxation time, International Journal Industrial Mathematics 1(4): 277-289.

[17] Othman M.I.A., Atwa S. Y., Farouk R.M., 2009, The effect of diffusion on two-dimensional problem of generalized thermoelasticity with Green–Naghdi theory 36(8): 857-864.

[18] Kumar R., Kaushal S., Milani A., 2010, Analysis of deformation due to various sources in micropolar thermodiffusive elastic medium, International Journal for Computational Methods in Engineering Science and Mechanics 11: 196–210.

[19] Kumar R., Singh B., 1998, Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space with stretch, Indian journal of Pure and applied math 29(6): 657-669.

[20] Eringen A.C., 1984, Plane waves in non-local micropolar elasticity, International Journal of Engineering Science 22:1113-1121.

[21] Thomas L., 1980,Fundamental of Heat Transfer, Prentice hall Inc-Englewmd Diffs, Newjersey.