On thermoelastic diffusion thin plate theory

doi:10.1007/s10483-015-1930-7

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (5): 619-632.doi: https://doi.org/10.1007/s10483-015-1930-7

On thermoelastic diffusion thin plate theory

M. AOUADI

Ecole Nationale d'Ingénieurs de Bizerte, University of Carthage, Carthage 1054, Tunisia

收稿日期:2014-10-06 修回日期:2015-01-28 出版日期:2015-05-01 发布日期:2015-05-01
通讯作者: M. AOUADI E-mail:moncefaouadi@yahoo.fr

On thermoelastic diffusion thin plate theory

M. AOUADI

Ecole Nationale d'Ingénieurs de Bizerte, University of Carthage, Carthage 1054, Tunisia

Received:2014-10-06 Revised:2015-01-28 Online:2015-05-01 Published:2015-05-01
Contact: M. AOUADI E-mail:moncefaouadi@yahoo.fr

摘要/Abstract

摘要：

The effect of diffusion on thermoelastic thin plates is investigated. The governing equations for thin thermoelastic diffusion plates under three different laws of heat and diffusion transmission are derived. By the C₀-semigroup theory, the well-posedness of the proposed equations is shown.

关键词: thin plate, thermoelastic diffusion, well-posedness

Abstract:

Key words: thin plate, thermoelastic diffusion, well-posedness

中图分类号:

M. AOUADI. On thermoelastic diffusion thin plate theory[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(5): 619-632.

参考文献

[1] Chadwick, P. On the propagation of thermoelastic disturbances in thin plates and rods. Journal of the Mechanics and Physics of Solids, 10, 99-109 (1962)
[2] Inan, E. Coupled theory of thermoelastic plates. Acta Mechanica, 14, 1-29 (1972)
[3] Timoshenko, S. and Woinowsky-Krieger, S. Theory of Plates and Shells, McGraw-Hill, New York (1987)
[4] Lagnese, J. E. and Lions, J. L. Modelling Analysis and Control of Thin Plates, Masson, Paris (1988)
[5] Norris, A. N. Dynamics of thermoelastic thin plates: a comparison of four theories. Journal of Thermal Stresses, 29, 169-195 (2006)
[6] Kim, J. U. On th energy decay of a linear thermoelastic bar and plate. SIAM Journal on Mathematical Analysis, 23, 889-899 (1992)
[7] Liu, Z. and Renardy, M. A note on the equation of a thermoelastic plate. Applied Mathematics Letters, 8, 1-6 (1995)
[8] Rivera, J. E. M. and Fatori, L. H. Regularizing properties and propagations of singularities for thermoelastic plates. Mathematical Methods in the Applied Sciences, 21, 797-821 (1998)
[9] Avalos, G. and Lasiecka, I. The null controllability of thermoelastic plates and singularity of the associated minimal energy function. Journal of Mathematical Analysis and Applications, 294, 34-61 (2004)
[10] Chai, S. and Guo, B. Z. Analyticity of a thermoelastic plate with variable coefficients. Journal of Mathematical Analysis and Applications, 354, 330-338 (2009)
[11] Liu, Z. and Quitanilla, R. Analyticity of solutions in type III thermoelastic plates. IMA Journal of Applied Mathematics, 75, 637-646 (2010)
[12] Zelati, M. C., Dell'Oro, F., and Pata, V. Energy decay of type III linear thermoelastic plates with memory. Journal of Mathematical Analysis and Applications, 401, 357-366 (2013)
[13] Nowacki, W. Dynamical problems of thermoelastic diffusion in solids I. Bulletin of the Polish Academy of Sciences Technical Sciences, 22, 55-64 (1974)
[14] Sherief, H., Hamza, F., and Saleh, H. The theory of generalized thermoelastic diffusion. International Journal of Engineering Science, 42, 591-608 (2004)
[15] Aouadi, M. The coupled theory of micropolar thermoelastic diffusion. Acta Mechanica, 208, 181-203 (2009)
[16] Aouadi, M. Theory of generalized micropolar thermoelastic diffusion under Lord-Shulman model. Journal of Thermal Stresses, 32, 923-942 (2009)
[17] Aouadi, M. A theory of thermoelastic diffusion materials with voids. Zeitschrift für Angewandte Mathematik und Physik, 61, 357-379 (2009)
[18] Aouadi, M. Qualitative results in the theory of thermoelastic diffusion mixtures. Journal of Thermal Stresses, 33, 595-615 (2010)
[19] Aouadi, M., Lazzari, B., and Nibbi, R. A theory of thermoelasticity with diffusion under Green-Naghdi models. Zeitschrift für Angewandte Mathematik und Mechanik, 94, 837-852 (2014)
[20] Aouadi, M., Lazzari, B., and Nibbi, R. Energy decay in thermoelastic diffusion theory with second sound and dissipative boundary. Meccanica, 48, 2159-2171 (2013)
[21] Aouadi, M. Classic and generalized thermoelastic diffusion theories. Encyclopedia of Thermal Stresses, Springer Science and Business Media, Dordrecht (2013)
[22] Cattaneo, C. Sulla conduzione del calore. Atti del Seminario Matematico e Fisico dell' Università di Modena, 3, 83-101 (1948)
[23] Gurtin, M. E. and Pipkin, A. C. A general theory of heat conduction with finite wave speeds. Archive for Rational Mechanics and Analysis, 31, 113-126 (1968)
[24] Ezzat, M. and Awad, E. Theory of heat and mass transfer in viscoelastic solids with microstructures. Journal of Thermal Stresses, 34, 795-816 (2011)
[25] Goldstein, J. A. Semigroups of Linear Operators and Applications, Oxford University Press, New York (1985)

On thermoelastic diffusion thin plate theory

On thermoelastic diffusion thin plate theory

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