Research ArticleOpen AccessGoogle Scholar indexed
On Rayleigh Wave in Two-Temperature Generalized Thermoelastic Medium without Energy Dissipation
Department of Mathematics, Post Graduate Government College, Chandigarh, India
Department of Mathematics, Government College, Haryana, India& Research Scholar in Mathematics, Singhania University, Rajasthan, India
- 1 Department of Mathematics, Post Graduate Government College, Chandigarh, India
- 2 Department of Mathematics, Government College, Haryana, India& Research Scholar in Mathematics, Singhania University, Rajasthan, India
Applied Mathematics·Volume 04 (2013)·Pages 107–112·Published 25 January 2013·DOI10.4236/am.2013.41019
Copy link · social · email
Abstract
In this paper, Rayleigh surface wave is studied at a stress free thermally insulated surface of a two-temperature thermoelastic solid half-space in absence of energy dissipation. The governing equations of two-temperature generalized thermoelastic medium without energy dissipation are solved for surface wave solutions. The appropriate particular solutions are applied to the required boundary conditions to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The non-dimensional speed is computed numerically and shown graphically to show the dependence on the frequency and two-temperature parameter.
KeywordsTwo-TemperatureGeneralized ThermoelasticityRayleigh WaveEnergy Dissipation
- H. Lord and Y. Shulman, “A Generalised 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
- A. E. Green and K. A. Lindsay, “Thermoelasticity,” Journal of Elasticity, Vol. 2, No. 1, 1972, pp. 1-7. doi:10.1007/BF00045689
- J. Ignaczak and M. Ostoja-Starzewski, “Thermoelasticity with Finite Wave Speeds,” Oxford University Press, Oxford, 2009.
- A. E. Green and P. M. Naghdi, “Thermoelasticity without Energy Dissipation,” Journal of Elasticity, Vol. 31, No. 3, 1993, pp. 189-208. doi:10.1007/BF00044969
- R. B. Hetnarski and J. Ignaczak, “Generalized Thermoelasticity,” Journal of Thermal Stresses, Vol. 22, No. 4-5, 1999, pp. 451-476. doi:10.1080/014957399280832
- 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. doi:10.1016/0022-5096(60)90035-1
- 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. doi:10.1080/01495739608946205
- 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, “Effect of Hydrostatic Initial Stresses on Waves in a Thermoelastic Solid Half-Space,” Applied Mathematics and Computation, Vol. 198, No. 2, 2008, pp. 494-505. doi:10.1016/j.amc.2007.08.072