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The current research deals with the analysis of reflection and refraction of plane wave at the imperfect boundary of two dissimilar transversely isotropic piezo-thermoelastic (PT) solid half-spaces with diffusion and two temperature. The formulation is applied in a 2-D model under the purview of three-phase lag (TPL) memory dependent derivative (MDD) heat transfer and TPL MDD diffusion. For the incident  QL  or  QTS  wave, there exist four coupled quasi reflected waves:  RQL  (reflected quasi-longitudinal),  RQMD  (reflected quasi-mass diffusion),  RQT  (reflected quasi thermal) and R QTS  (reflected quasi-transverse) and four transmitted waves:  TQL  (transmitted quasi-longitudinal),  TQMD  (transmitted quasi-mass diffusion),  TQT  (transmitted quasi thermal) and  TQTS  (transmitted quasi-transverse) waves propagating with different speeds in two solid half-spaces. The expressions for the amplitude ratios and energy ratios are calculated for the reflected and refracted waves. Calculations for normal force stiffness, transverse force stiffness, thermal contact conductance and welded boundaries are also done as particular cases. Some special cases are also discussed. MATLAB software is used for the numerical and graphical analysis and to show the effect of two-temperature on the amplitude ratios of different reflected and refracted waves for incident QL and QTS waves.

waves in random and complex media

Reflection and refraction of plane wave in piezo-thermoelastic diffusive half spaces with three phase lag memory dependent derivative and two-temperature