Effects of Relaxation Times and Inclined Angles on a Material with Corrugation under Magneto-Thermal Stress

Abstract

The current research deals with the Mathematical solutions for the thermo-mechanical response of surface waves on a half-space with an inclined mechanical load on the corrugated-impedance surface influenced by magnetic field and thermal stress. We utilized the harmonic approach for wave analysis in determining the solution of the model. Using Green and Lindsay theory of thermoelasticity, the distribution fields of the system such as the thermal, normal and shear stresses, and the displacement components were analytically derived. Also, the behavior of the two times relaxation constants, special angles of various inclinations and the effect of magnetism, etc., on the distributions are graphically presented using MATHEMATICA 11 software. Our computational results show that an increase in the inclined angles (special and non-special angles) produces a corresponding increase in the distribution profiles of the surface wave. Also, increase in one of the thermal relaxation constants exhibited decreasing effects on the distribution profiles whilst the temperature profile increases in modulation. Thus, our result holds true for the thermal assumptions of the temperature distribution under the considered thermo-elasticity model. Also, researchers working in the area of non-destructive material testing and evaluation would find this investigation useful; owing to the grooved-impedance coloration of the material surface and the model in its entirety.

Keywords: Relaxation times, impedance boundary, special angle of inclination, grooved boundary, magneto-thermal effects.

2010 Mathematics Subject Classification. 26A25; 26A35