Rayleigh waves in graded thermoelastic media with fractional heat conduction: A sensitivity-based approach

The propagation of Rayleigh waves is critical for understanding and improving the resilience of engineering structures like earthquake-resistant foundations, nuclear reactor cooling systems, and high-speed aeronautical components. This study investigates the complex behavior of these surface waves in a rotating, functionally graded semiconductor half-space, a configuration common in advanced technologies but not yet fully understood under coupled thermal-mechanical constraints. A novel thermoelastic model is developed using the Caputo fractional derivative to generalize the three-phase-lag heat conduction theory, effectively capturing memory effects and anomalous thermal diffusion often absent in classical models. The material properties of the semiconductor medium are considered to vary continuously with depth, reflecting the nature of functionally graded materials. The governing equations are solved to derive a secular equation for Rayleigh waves. Key propagation characteristics including phase velocity, attenuation coefficient, specific heat loss, and penetration depth are analyzed numerically for silicon. A normalized local sensitivity analysis identifies the rotational frequency as the most influential parameter on wave dynamics. The results demonstrate that increasing the material gradation parameter and rotational frequency significantly enhances phase velocity and penetration depth while reducing wave attenuation and thermal dissipation. These findings provide fundamental insights into wave-thermoelastic interactions and offer practical guidelines for optimizing material properties in semiconductor device design, geophysical exploration, and thermal management systems.