The present paper is concerned with the propagation of plane waves in an isotropic two-temperature generalized thermoelastic solid half-space in context of Green and Naghdi theory of type II (without energy dissipation). The governing equations in x – z plane are solved to show the existence of three coupled plane waves. The reflection of plane waves from a thermally insulated free surface is considered to obtain the relations between the reflection coefficients. A particular example of the half-space is chosen for numerical computations of the speeds and reflection coefficients of plane waves. Effects of two-temperature and rotation parameters on the speeds and the reflection coefficients of plane waves are shown graphically.
H. Deresiewicz, “Effect of Boundaries on Waves in a Thermo-Elastic Solid: Reflection of Plane Waves from Plane Boundary,” Journal of the Mechanics and Physics of Solids, Vol. 8, No. 3, 1960, pp. 164-172.
A. N. Sinha, and S. B. Sinha, “Reflection of Thermoelastic Waves at a Solid Half Space with Thermal Relaxation,” Journal of Physics of the Earth, Vol. 22, No. 2, 1974, pp. 237-244. doi:10.4294/jpe1952.22.237
S. B. Sinha and K. A. Elsibai, “Reflection of Thermoelastic Waves at a Solid Half-Space with Two Thermal Relaxation Times,” Journal of Thermal Stresses, Vol. 19, No. 8, 1996, pp. 763-777.
S. B. Sinha and K. A. Elsibai, “Reflection and Refraction of Thermoelastic Waves at an Interface of two Semi-Infinite Media with Two Thermal Relaxation Times,” Journal of Thermal Stresses, Vol. 20, No. 2, 1997, pp. 129-146. doi:10.1080/01495739708956095
J. N. Sharma, V. Kumar and D. Chand, “Reflection of Generalized Thermoelastic Waves from the Boundary of a Half-Space,” Journal of Thermal Stresses, Vol. 26, No. 10, 2003, pp. 925-942. doi:10.1080/01495730306342
M. I. A. Othman and Y. Song, “Reflection of Plane Waves from an Elastic Solid Half-Space under Hydrostatic Initial Stress without Energy Dissipation,” International Journal of Solids and Structures, Vol. 44, No. 17, 2007, pp. 5651-5664. doi:10.1016/j.ijsolstr.2007.01.022
B. Singh, “Reflection of Plane Waves at the Free Surface of a Monoclinic Thermoelastic Solid Half-Space,” European Journal of Mechanics—A/Solids, Vol. 29, No. 5, 2010, pp. 911-916.
P. J. Chen, M. E. Gurtin and W. O. Williams, “On the Thermodynamics of Non-Simple Elastic Materials with Two Temperatures,” Zeitschrift für angewandte Mathe matik und Physik, Vol. 20, No. 1, 1969, pp. 107-112.
P. Puri and P. M. Jordan, “On the Propagation of Har monic Plane Waves under the Two-Temperature Theory,” International Journal of Engineering Science, Vol. 44, No. 17, 2006, pp. 1113-1126.
R. Quintanilla and P. M. Jordan, “A Note on the Two Temperature Theory with Dual-Phase-Lag Delay: Some Exact Solutions,” Mechanics Research Communications, Vol. 36, No. 7, 2009, pp. 796-803.
R. Kumar and S. Mukhopadhyay, “Effects of Thermal Relaxation Time on Plane Wave Propagation under Two-Temperature Thermoelasticity,” International Journal of Engineering Science, Vol. 48, No. 2, 2010, pp. 128-139.
A. Magana and R. Quintanilla, “Uniqueness and Growth of Solutions in Two-Temperature Generalized Thermoelastic Theories,” Mathematics and Mechanics of Solids, Vol. 14, No. 7, 2009, pp. 622-634.