The Effect of the Impedance Limit on the Reflection of Plane Waves in a Micropolar Thermoviscoelastic Material Using A Modified Green-Lindsay Model
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Abstract
A new mathematical framework is used to look into how plane waves move through a micropolar thermoviscoelastic half-space using the modified Green-Lindsay (MG-L) generalized theory of thermoelasticity and impedance boundaries. With the right amounts, the controlling equations for the two-dimensional case become dimensionless. To make things even easier, the potential function method is used to separate the set of equations. The plane wave (longitudinal displacement (LD) wave, temperature (T) wave, coupled transverse displacement (CD I) wave, or coupled transverse microrotational (CD II) wave) hits the model, and four waves are reflected: LD, T, CD I, and CD II. For the impedance border, the amplitude ratios of these reflected waves are found compared to the wave that came in (LD or T or CD I or CD II). The amplitude ratios that are found depend on the frequency, the angle of incidence, and on the physical qualities of the medium. A graph shows how the factors of viscosity and impedance change the amplitude ratios. Due to this study, some special cases have been cut down. The results obtained can be used to develop new materials, which can be used to investigate coupled transverse and microrotation waves as well as coupled longitudinal and thermal waves.
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