Reflection phenomena of plane waves in double-porosity fractional thermoelastic half-space under initial stress and rotation

Abstract

This study investigates the reflection of two-dimensional plane waves in an initially stressed, rotating orthotropic half-space with double porosity formulated within the framework of the Lord–Shulman generalized thermoelasticity theory under fractional-order derivative. Five distinct reflected waves are considered: quasi longitudinal-P (qP), quasi shear vertical (qSV), voids of type-I and type-II, and quasi-thermal (qT). The governing equations of motion and constitutive relations are derived leading to characteristic equations for phase velocity and attenuation coefficients. Analytical expressions for reflection coefficients and energy ratios are also obtained which provide a comprehensive description of the reflection phenomena. Numerical simulations performed using Python demonstrate that phase velocity, reflection coefficients, and energy ratios depend strongly on frequency, wave number, rotation, initial stress, and fractional-order parameters. Notably, initial stress suppresses low-frequency propagation, reducing qP-wave velocities by approximately 14–\(18\%\), while enhancing high-frequency propagation with a 9–\(12\%\) increase. These results underscore the essential influence of double porosity and fractional-order thermoelasticity on wave behavior and highlight the study’s relevance to applications in geophysics, seismic wave analysis, and materials engineering.