Two-Temperature Effects on Plane Waves in Generalized Thermo-Microstretch Elastic Solid

In this article, the effect of two temperatures on plane waves propagating through a generalized-thermo-microstretch elastic half-space solid has been investigated. The surface of the medium is subjected to a mode-I crack, and the $z$ axis is pointing vertically into the medium. Two fascinating theories of generalized thermo-elasticity presented by Green and Naghdi and named as without energy dissipation (GN-II) and with energy dissipation (GN-III) have been used. Governing equations for each particular case are also derived, and a solution is obtained. An analytical technique of normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, the temperature, and the couple stresses distribution. The variations of the considered variables against the vertical distance are illustrated graphically. Comparisons are made with the results between type II and III in generalized-thermo-microstretch and in a particular case (without microstretch constants). Numerical work is also performed for a suitable material with the aim of illustrating the results. It is found that the maximum amplitude is obtained for the maximum value of the two temperature parametric constant.