THE EFFECT OF DUAL-PHASE-LAG MODEL ON REFLECTION OF THERMOELASTIC WAVES IN A SOLID HALF SPACE WITH VARIABLE MATERIAL PROPERTIES

• Published in: Acta mechanica solida Sinica Vol. 26; no. 6; pp. 659 - 670
• Main Authors: Zenkour, A.M., Mashat, D.S., Abouelregal, A.E.
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier Ltd 01.12.2013; Springer Singapore; Department of Mathematics, Faculty of Science, King Abdulaziz University,P.O.Box 80203, Jeddah 21589, Saudi Arabia; Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt%Department of Mathematics, Faculty of Science, King Abdulaziz University,P.O.Box 80203, Jeddah 21589, Saudi Arabia%Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt; Department of Mathematics, College of Science and Arts, University of Aljouf, El-Qurayat, Saudi Arabia
• Subjects: Amplitudes; Boundaries; Classical Mechanics; dual-phase-lag; Engineering; generalized thermoelasticity; Half spaces; Mathematical analysis; Mathematical models; Modulus of elasticity; Reflection; reflection waves; Surfaces and Interfaces; Theoretical and Applied Mechanics; Thermoelasticity; Thin Films; variable material properties; 反射波; 可变; 固体; 弹性半空间; 弹性波; 材料性质; 模型; 相位滞后; generalized thermoelasticity; variable material properties; reflection waves; dual-phase-lag
• ISSN: 0894-9166; 1860-2134
• DOI: 10.1016/S0894-9166(14)60009-4

The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity： Lord-Shulman （L-S） theory with one relaxation time, Green-Naghdi （G-N） theory without energy dissipation and Tzou theory with dual-phase-lag （DPL）, as well as the coupled thermoelasticity （CTE） theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.