<p>This study investigates the reflection of plane waves in an initially stressed rotating orthotropic microstretch thermoelastic half-space within the frameworks of Lord–Shulman (LS) and Green–Lindsay (GL) theories. A complete mathematical model is formulated to describe the coupled effects of displacement, microrotation, microstretch and thermal fields. When a quasi-longitudinal displacement (qLD) wave strikes the stress-free thermally insulated boundary it generates five reflected wave modes: qLD, quasi-transverse displacement (qTD), quasi-transverse microrotational (qTM), quasi-longitudinal microstretch (qLM) and quasi-thermal (qT) waves. Analytical expressions for phase velocities, reflection coefficients and energy ratios are derived and these quantities are evaluated numerically. Graphical results are used to study how initial stress and rotation influence the phase velocity and reflection coefficients. The graphical results reveal significant differences between LS and GL theories particularly in the behavior of phase velocity and reflection coefficients under initial stress and rotation. The study demonstrates that thermal relaxation times in the GL theory considerably alter the reflection patterns while the LS theory shows stronger sensitivity to mechanical effects. To establish the accuracy of the formulation the governing equations are reduced by setting initial stress, rotation and thermal parameters to zero. In this limiting case, the model exactly agrees with the pre-established results which confirms the correctness of the derived boundary-value system. A benchmark comparison table and graphical evaluation further validate the present results. The findings provide new insights into wave propagation in micro-structured thermoelastic media and offer a reliable framework for applications in geophysics, materials engineering and advanced wave-based analysis.</p>

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Reflection of plane waves in an initially stressed rotating orthotropic microstretch structure under generalised thermo-elasticity

  • Deepak Kumar,
  • Brijendra Paswan,
  • Prakriti Kundu,
  • Harsita Kumari

摘要

This study investigates the reflection of plane waves in an initially stressed rotating orthotropic microstretch thermoelastic half-space within the frameworks of Lord–Shulman (LS) and Green–Lindsay (GL) theories. A complete mathematical model is formulated to describe the coupled effects of displacement, microrotation, microstretch and thermal fields. When a quasi-longitudinal displacement (qLD) wave strikes the stress-free thermally insulated boundary it generates five reflected wave modes: qLD, quasi-transverse displacement (qTD), quasi-transverse microrotational (qTM), quasi-longitudinal microstretch (qLM) and quasi-thermal (qT) waves. Analytical expressions for phase velocities, reflection coefficients and energy ratios are derived and these quantities are evaluated numerically. Graphical results are used to study how initial stress and rotation influence the phase velocity and reflection coefficients. The graphical results reveal significant differences between LS and GL theories particularly in the behavior of phase velocity and reflection coefficients under initial stress and rotation. The study demonstrates that thermal relaxation times in the GL theory considerably alter the reflection patterns while the LS theory shows stronger sensitivity to mechanical effects. To establish the accuracy of the formulation the governing equations are reduced by setting initial stress, rotation and thermal parameters to zero. In this limiting case, the model exactly agrees with the pre-established results which confirms the correctness of the derived boundary-value system. A benchmark comparison table and graphical evaluation further validate the present results. The findings provide new insights into wave propagation in micro-structured thermoelastic media and offer a reliable framework for applications in geophysics, materials engineering and advanced wave-based analysis.