Reflection of Plane Waves from a Micropolar Fractional Thermoelastic Solid with Initial Stress and Magnetic Field

The governing equations for initial stress and magnetic field in linear, isotropic, homogeneous, and micropolar fractional order thermoelasticity are obtained. For solutions involving plane harmonic waves, the governing equations are solved. Four distinct-speed plane waves are found to exist, according to two different velocity equations. A stress-free boundary problem involving the reflection of plane waves from an isothermal, thermally insulated surface is examined. The boundary conditions at a plane surface are satisfied by the formulation of appropriate potentials for incident and reflected waves. A relationship is found between the reflection coefficients for different types of reflected waves. The reflection coefficients for different reflected waves are computed for pertinent material properties, as an example. Graphical representations are provided to illustrate the effects of fractional order thermoelasticity, initial stress, magnetic field, phase velocity, specific loss, and attenuation coefficients against angle of incidence.