Abstract In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.

Rajneesh Kumar, Vandana Gupta Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative 2013 Chin. Phys. B 22 074601

[1]

Nowacki W 1974 Bulletin of Polish Academy of Sciences Series, Science and Technology 22 55

[2]

Nowacki W 1974 Bulletin of Polish Academy of Sciences Series, Science and Technology 22 129

[3]

Nowacki W 1974 Bulletin of Polish Academy of Sciences Series, Science and Technology 22 275

[4]

Nowacki W 1974 Proc. Vib. Prob. 15 105

[5]

Sherief H H and Saleh H 2005 Int. J. of Solids and Struct 42 4484

[6]

Kumar R and Kansal T 2008 Int. J. Solids and Struct 45 5890

[7]

Kumar R and Chawla V 2011 Int. Commun. Heat Mass Transfer 38 456

[8]

Povstenko Y Z 2005 J. Therm. Stress 28 83

[9]

Povstenko Y Z 2009 J. Mathematical Stresses 162 296

[10]

Youssef H M 2010 J. Heat Transfer 132 1

[11]

Jiang X Y and Xu M Y 2010 Physica A 389 3368

[12]

Povstenko Y Z 2010 Mech. Res. Commun. 37 436

[13]

Ezzat M A 2011 Physica B 406 30

[14]

Jumarie G 2010 Comput. Math. Appl. 59 1142

[15]

Ezzat M A 2011b Applied Mathematical Modelling 35 4965

[16]

Povstenko Y Z 2011 J. Therm. Stress 34 97

[17]

Biswas R K and Sen S 2011 Journal of Vibration and Control 17 1034

[18]

Jiang X Y and Qi H T 2012 J. Phys. A: Math. Theor. 45 485101

[19]

Iesan D 1986 Acta Mechanica 60 67

[20]

Sherief H H, Saleh H and Hamza F 2004 International Journal of Engineering Science 42 591

[21]

Aouadi M 2007 J. Therm. Stress 30 665

[22]

Aouadi M 2008 J. Therm. Stress 31 270

[23]

Sherief H H, El-Said A and Abd El Latief A 2010 Int. J. Solids and Struct. 47 269

[24]

El-Karmany A S and Ezzat M A 2011 J. Therm. Stress 34 264

[25]

Catteneo C 1958 C. R. Acad. Sci. 247 431

[26]

Poon Y M, Wei E B and Gu G 2010 Chin. Phys. B 19 096201

[27]

Sharma M D 2010 Acta Mechanica 209 275

[28]

Abbas I A, Kumar R and Chawla V 2012 Chin. Phys. B 21 084601

[29]

Abbas I A and Othman M I A 2012 Chin. Phys. B 21 014601

[30]

Lotfy K 2012 Chin. Phys. B 21 064214

[31]

Lotfy K and Othman M I A 2011 Chin. Phys. B. 20 074601

[32]

Miller K S and Ross B 1993 An Introduction to the Fractional Integrals and Derivatives, Theory and Applications (New York: John Wiley and Sons)

[33]

Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)

[34]

Kuang Z B 2010 Acta Mech. 214 275

[35]

Biot M A 1956 J. Appl. Phys. 27 240

[36]

Aouadi M 2007 J. Therm. Stress 30 665

[37]

Churchill R V 1972 Operational Mathematics (3rd edn.) (New York: McGraw-Hill)

[38]

Slaughter W S 2002 The Linearised Theory of Elasticity (1st edn.) (New York: Birkhauser Boston)

[39]

Kolsky H 1963 Stress Waves in Solids (Oxford: Clarendon Press)

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