Two Temperature Heat Flux of Semi Infinite Piezoelectric Ceramic Rod

Essam Bassiouny, Refaat Sabry, Hamdy Youssef

Faculty of Science and Humanitarian Studies, Salman Bin Abdulaziz University, Al-Kharj, KSA.
Mechanical Engineering Department, Faculty of Engineering and Islamic Architecture, Umm Al-Qura University, Mecca, KSA.

DOI: 10.4236/eng.2013.53038                

Abstract

The theory of two-temperature generalized thermoelasticity is used to solve the problem of heating a semi-infinite rod made of a piezoelectric ceramic material within the framework of generalized thermopiezoelasticity theory by supplying the rod a certain amount of heat uniformly distributed over a finite time period to the finite end of the rod. The Laplace transform formalism is used to solve the proposed model. Inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. The physical parameters (i.e., conductive temperature, dynamical temperature, stress, strain, and displacement distributions) are investigated graphically.

Keywords

Two Temperatures; Generalized Thermoelasticity; Thermopiezoelasticity; Thermal Waves; Ceramics; Piezoelectric Materials—Heat Flux

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. Tani, T. Takagi and J. Qiu, “Intelligent Material Systems: Application of Functional Materials,” Applied Mechanics Review, Vol. 51, No. 8, 1998, pp. 505-521. doi:10.1115/1.3099019
[2]	H. S. Tzou, “Multifield Transducers, Devices, Mechatronics Systems and Structronic Systems with Smart Materials,” The Shock and Vibration Digest, Vol. 30, No. 4, 1998, pp. 282-294. doi:10.1177/058310249803000402
[3]	S. S. Rao and M. Sunar, “Piezoelectricity and Its Use in Disturbance Sensing and Control of Flexible Structures: A Survey,” Applied Mechanics Review, Vol. 47, No. 4, 1994, pp. 113-123. doi:10.1115/1.3111074
[4]	H. W. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” Journal of the Mechanics and Physics of Solids, Vol. 15, No. 5, 1967, pp. 299-309. doi:10.1016/0022-5096(67)90024-5
[5]	A. E. Green and K. E. Lindsay, “Thermoelasticity,” Journal of Elasticity, Vol. 2, No. 1, 1972, pp. 1-7. doi:10.1007/BF00045689
[6]	E. Bassiouny and H. Youssef, “Two-Temperature Generalized Thermopiezoelasticity of Finite Rod Subjected to Different Types of Thermal Loading,” Journal of Thermal Stresses, Vol. 31, No. 3, 2008, pp. 233-245. doi:10.1080/01495730701737902
[7]	T. H. He, X. G. Tian and Y. P. Shen, “State Space Approach to One-Dimensional Shock Problem for a SemiInfinite Piezoelectric Rod,” International Journal of Engineering Science, Vol. 40, No. 10, 2002, pp. 1081-1097. doi:10.1016/S0020-7225(02)00005-8
[8]	G. Hanig and U. Hirdes, “A Method for the Numerical Inversion of Laplace Transform,” Journal of Computational and Applied Mathematics, Vol. 10, No. 1, 1984, pp. 113-132. doi:10.1016/0377-0427(84)90075-X