References
1. Levine, I.N., Physical Chemistry, 6th Ed., McGraw
Hill, New York (2009).
2. Kumar, S., Yildirim, A., Khan, Y., and Wei, L.
A fractional model of the di usion equation and its
analytical solution using Laplace transform", Scientia
Iranica B, 19(4), pp. 1117-1123 (2012).
3. Kuang, Z.B. Some variational principles in elastic dielectric
and elastic magnetic material", European Journal
of Mechanics-A/Solids, 27, pp. 504-514 (2008).
4. Kuang, Z.B. Variational principles of generalized dynamical
theory of thermopiezoelectricity", Acta Mech.,
203, pp. 1-11 (2009).
5. Yang, Q.S., Qin, Q.H., Ma, L.H., Lu, X.Z., and Cui,
C.Q. A theoretical model and nite element formulation
for coupled thermo-electro-chemo-mechanical media",
Mechanics of Materials, 42, pp. 148-156 (2010).
6. Kuang, Z.B. Internal energy variational principle
and governing equations in electroelastic analysis",
International Journal of Solids and Structures, 46, pp.
902-911 (2009).
7. Branco, J.R., Ferreira, J.A., and da Silva, P. Non-
Fickian delay reaction-di usion equation: Theoretical
and numerical study", Applied Numerical Mathematics,
60, pp. 531-549 (2010).
8. Peret, T., Clement, A., Freour, S., and Jacquemin,
F. Numerical transient hygro-elastic analyses of reinforced
Fickian and non-Fickian polymers", Composite
Structures, 116, pp. 395-403 (2014).
9. Barbeiro, S., Bardeji, S.G.H., and Ferreira, J.A.
Laplace transform- nite element method for non-
Fickian
ows", Computer Methods in Applied Mechanics
and Engineering, 261-262, pp. 16-23 (2013).
10. Kuang, Z.B. Variational principles for generalized
thermodi usion theory in pyroelectricity", Acta Mech.,
214, pp. 275-289 (2010).
11. Lord, H.W. and Shulman, Y. A generalized dynamical
theory of thermoelasticity", Journal of the Mechanics
and Physics of Solids, 15, pp. 299-309 (1967).
12. Green, A.E. and Lindsay, K.A. Thermoelasticity",
Journal of Elasticity, 2, pp. 1-7 (1972).
13. Green, A.E. and Naghdi, P.M. Thermoelasticity without
energy dissipation", Journal of Elasticity, 31, pp.
189-208 (1993).
14. Guo, S.H. The comparisons of thermo-elastic waves
for Lord-Shulman mode and Green-Lindsay mode
based on Guo's eigen theory", Acta Mech., 222, pp.
199-208 (2011).
15. Hosseini, S.M. and Abolbashari, M.H. Analytical
solution for thermoelastic waves propagation analysis
in thick hollow cylinder based on Green-Naghdi
model of coupled thermoelasticity", Journal of Thermal
Stresses, 35, pp. 363-376 (2012).
16. Hosseini, S.M. Coupled thermoelasticity and second
sound in nite length functionally graded thick hollow
cylinders (without energy dissipation)", Materials and
Design, 30, pp. 2011-2023 (2009).
17. Hosseini, S.M. Shock-induced thermoelastic wave
propagation analysis in a thick hollow cylinder without
energy dissipation using mesh-free generalized nite
di erence (GFD) method", Acta Mech., 224, pp. 465-
478 (2013).
18. Lee, Z.Y. Generalized coupled transient thermoelastic
problem of multilayered hollow cylinder with hybrid
boundary conditions", International Communications
in Heat and Mass Transfer, 33, pp. 518-528 (2006).
19. Xia, R., Tian, X., and Shen, Y. Dynamic response
of two-dimensional generalized thermoelastic coupling
problem subjected to a moving heat source", Acta
Mechanica Solida Sinica, 27, pp. 300-305 (2014).
20. Shariyat, M. Nonlinear transient stress and wave
propagation analyses of the FGM thick cylinders, employing
a uni ed generalized thermoelasticity theory",
International Journal of Mechanical Sciences, 65, pp.
24-37 (2012).
21. Shariyat, M., Lavasani, S.M.H., and Khaghani, M.
Nonlinear transient thermal stress and elastic wave
propagation analyses of thick temperature-dependent
FGM cylinders using a second-order point-collocation
method", Applied Mathematical Modelling, 34, pp.
898-918 (2010).
22. Shariyat, M., Khaghani, M., and Lavasani, S.M.H.
Nonlinear thermoelasticity, vibration, and stress wave
propagation analyses of thick FGM cylinders with
temperature-dependent material properties", European
Journal of Mechanics - A/Solids, 29, pp. 378-391
(2010).
23. Bagri, A. and Eslami, M.R. A uni ed generalized
thermoelasticity, solution for cylinders and spheres",
International Journal of Mechanical Sciences, 49, pp.
1325-1335 (2007).
24. Bagri, A. and Eslami, M.R. A uni ed generalized
thermoelasticity formulation; application to thick
functionally graded cylinders", Journal of Thermal
Stresses, 30, pp. 911-930 (2007).
25. Sherief, H.H. and Abd El-Latief, A.M. Application
of fractional order theory of thermoelasticity to a 2D
problem for a half-space", Applied Mathematics and
Computation, 248, pp. 584-592 (2014).
26. Hosseini, S.A., Abolbashari, M.H., and Hosseini, S.M.
Shock induced molar concentration wave propagation
and coupled non-Fick di usion-elasticity analysis using
an analytical method", Acta Mech., 225, pp. 3591-
3599 (2014).
2086 S.A. Hosseini et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2077{2086
27. Kumar, R. and Chawla, V. A study of fundamental
solution in orthotropic thermodi usive elastic media",
International Communications in Heat and Mass
Transfer, 38, pp. 456-462 (2011).
28. Deswal, S. and Choudhary, S. Impulsive e ect on
an elastic solid with generalized Thermodi usion",
Journal of Engineering Mathematics, 63, pp. 79-94
(2009).
29. Aouadi, M. Uniqueness and reciprocity theorems
in the theory of generalized thermoelastic di usion",
Journal of Thermal Stresses, 30, pp. 665-678 (2007).
30. Aouadi, M. Qualitative aspects in the coupled theory
of thermoelastic di usion", Journal of Thermal
Stresses, 31, pp. 706-727 (2008).
31. Singh, B., Singh, L., and Deswal, S. Re
ection
of plane waves in thermo-di usion elasticity without
dissipation under the e ect of rotation", Mechanics
of Advanced Materials and Structures, 23, pp. 74-79
(2016).
32. Allam, A.A., Omar, M.A., and Ramadan, K.T. A
thermoelastic di usion interaction in an in nitely long
annular cylinder", Archive of Applied Mechanics, 84,
pp. 953-965 (2014).
33. Suo, Y. and Shen, S. Dynamical theoretical model
and variational principles for coupled temperaturedi
usion-mechanics", Acta Mech, 223, pp. 29-41
(2012).
34. Suo, Y. and Shen, S. Analytical solution for onedimensional
coupled non-Fick di usion and mechanics",
Archive of Applied Mechanics, 83, pp. 397-411
(2013).
35. Hosseini, S.M., Sladek, J., and Sladek, V. Two
dimensional analysis of coupled non-Fick di usionelastodynamics
problems in functionally graded materials
using meshless local Petrov-Galerkin (MLPG)
method", Applied Mathematics and Computation,
268, pp. 937-946 (2015).
36. Hosseini, S.M., Sladek, J., and Sladek, V. Two dimensional
transient analysis of coupled non-Fick di usionthermoelasticity
based on Green-Naghdi theory using
the meshless local Petrov-Galerkin (MLPG) method",
International Journal of Mechanical Sciences, 82, pp.
74-80 (2014).
37. Cohen, A.M., Numerical Methods for Laplace Transform
Inversion, Springer US (2007).
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