Reflection of a plane magneto-thermoelastic wave at the boundary of a solid half-space in presence of initial stress

The paper studies the effects of the magnetic field and initial stress on the reflection of a plane magneto-thermoelastic wave from the boundary of a solid half-space. The basic dynamical equations of thermoelasticity in presence of Lorentz force and the heat conduction equation of Green–Lindsay theory have been solved to derive the wave equations for the reflected P-, SV- and thermal waves. By considering the boundary to be a stress-free and insulated one, the boundary equations that contain the ratios of the amplitude of the reflected components to that of the incident wave have been obtained. The analytical solution has been cast in matrix form for each of the incident plane waves at the boundary, namely the P-wave, SV-wave and thermal wave. The numerical calculations of the absolute values of the amplitude ratios for an incident SV-wave have been carried out for different values of both magnetic pressure number and initial stress parameter. The initial stress parameter shows a marked influence on the magnitude of the amplitude ratios. The reflection coefficients for different values of magnetic pressure number in absence of initial stress have also been included for the sake of comparison.