Two-Temperature Generalized Thermopiezoelasticity for One Dimensional Problems – State Space Approach

• Autorzy: Youssef H. M. , Bassiouny E.
• Języki publikacji: EN

Abstrakty

EN

The theory of two-temperature generalized thermoelasticity, based on the theory of Youssef is used to solve boundary value problems of one dimensional piezoelectric half-space with heating its boundary with different types of heating. The governing equations are solved in the Laplace transform domain by using state-space approach of the modern control theory. The general solution obtained is applied to a specific problems of a half-space subjected to three types of heating; the thermal shock type, the ramp type and the harmonic type. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. The conductive temperature, the dynamical temperature, the stress and the strain distributions are shown graphically with some comparisons.

Słowa kluczowe

EN

piezoelectric material; generalized thermoelasticity; two-temperature; state space

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2008
• Tom: Vol. 14, nr 1
• Strony: 55--64
• Opis fizyczny: Bibliogr. 24 poz., rys.

Twórcy

autor

Youssef H. M.

autor

Bassiouny E.

• Faculty of Engineering, Umm Al-Qura University, PO. Box 5555, Makkah, Saudi Arabia,

Bibliografia

• [1] H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids 15, 299-309 (1967).
• [2] N. Naotak, R. Hetnarski and Y. Tanigawa, (2003), Thermal Stresses (2nd Edition), Taylor & Francis, New York.
• [3] J. Ignaczak and A Note, On Uniqueness in Thermoelasticity With One Relaxation Time, J. Thermal Stresses 5, 257-263 (1982).
• [4] Müller, The coldness, A universal function in thermoelastic solids, Arch. Ration. Mech. An. 41, 319-332 (1971).
• [5] Ahmed S. El-Karamany and Magdy A. Ezzat, Thermal shock problem in generalized thermo-viscoelasticty under four theories, Int. J. of Eng. Sci. 42(7) 649-671 (2004).
• [6] A. E. Green and K. E. Lindsay, Thermoelasticity, J. Elasticity 2, I-7 (1972).
• [7] D. Y. Tzou, Macro- to microscale heat transfer: the lagging behavior, Taylor & Francis, Washington (1997) DC.
• [8] R. D. Mindlin, On the equations of motion of piezoelectric crystals, in: N. I. Muskilishivili, Problems of continuum Mechanics, 70th Birthday Volume, SIAM, Philadelphia, 282-290 (1961).
• [9] R. D. Mindlin, Equations of high frequency vibrations of thermo-piezoelectric plate, Int. J. Solids Struct. 10, 625-637 (1974).
• [10] W. Nowacki, Some general theorems of thermo-piezoelectricity, J. Therm. Stress. 1, 171-182 (1978).
• [11] W. Nowacki, Foundations of linear piezoelectricity, in: H. Parkus (Ed), Electromagnetic interactions in Elastic Solids, Springer, Wein, Chapter 1. (1979).
• [12] D. S. Chandrasekharaiah, A generalized thermoelastic wave propagation in a semi-infinite piezoelectric rod, Acta Mech. 71, 39-49 (1988).
• [13] M. C. Majhi, Discontinuities in generalized thermoelastic wave propagation in a semi-infinite piezoelectric rod, J. Tech. Phys. 36, 269-278 (1995).
• [14] J. N. Sharma, M. Kumar, Plane harmonic waves in piezo-thermoelastic materials, Indian Eng. Mater. Sci. 7, 434-442 (2000).
• [15] E. Bassiouny and A. F. Gahleb, A one dimensional problem in the generalized theory of thermopiezoelasticity, In: G. A. Maugin (Ed), The mechanical behavior of electromagnetic solid continua, Elsevier science publisher B. V. (North Holland), IUTAM-IUPAP, 79-84 (1984).
• [16] H. Tianhu, T. Xiaogeneg and S. Yapeng, State space approach to one-dimensional shock problem for a semiinfinite piezoelectric rod, Int. J. Eng. Sci. 40, 1081-1097 (2002).
• [17] H. Tianhu, T. Xiaogeneg and S. Yapeng, Two-dimensional generalized thermal shock a thick piezoelectric plate of infinite extent, Int. J. Eng. Sci. 40, 2249-2264 (2002).
• [18] B. Singh, Wave propagation in an anisotropic generalized thermoelastic solid, Indian J. Pure Appl. Math. 34,1479-1485 (2003).
• [19] H. Youssef, Theory of Two-Temperature Generalized Thermoelasticity, IMA Journal of Applied Mathematics, IMA J. Appl. Math. 71(3), 383-390 (2006).
• [20] H. Youssef, Problem of Generalized Thermoelastic Infinite Medium with Cylindrical Cavity Subjected to a Ramp-Type Heating and Loading, Archive Appl. Mech.75, 553-565 (2006).
• [21] L. Y. Bahar and R. B. Hetnarski, State Space Approach to Thermoelasticity, J. Thermal Stresses 1, 135 (1978).
• [22] S. Mukhopadhyay, Thermoelastic interactions without energy dissipation in an unbounded body with a spherical cavity subjected to harmonically varying temperature, J. Mech. Res. Comm. 31, 81-89 (2004).
• [23] G. Hanig and U. Hirdes, A method for the numerical inversion of Laplace transform, J. Comp. Appl. Math. 10, 113-132 (1984).
• [24] H. Chu, C. Chen and C. Weng, Applications of Fourier series Technique to transient heat transfer, Chem. Eng. Commun. 16, 215-227 (1982).