Influence of Initial Stress on Wave Propagation in Microelongated Thermo-Elastic Media Under the Refined Fractional Dual Phase Lag Model

This paper focuses on analyzing how initial stress influences wave propagation phenomena in a microelongated thermoelastic medium described within the framework of fractional conformable derivative, considering both the dual phase lag (DPL) and refined dual phase lag (RDPL) theories. The fundamental governing equations for heat transfer, mechanical motion, and microelongation are established to incorporate finite thermal wave speed and microelongation effects. Through an appropriate non-dimensionalization procedure and the application of the normal mode analysis technique, the coupled partial differential system is transformed into a form that admits explicit analytical solutions. These solutions provide expressions for displacement, microelongation, temperature distribution, and stress components, allowing a comprehensive examination of the thermomechanical wave behavior within the medium. To better comprehend the theoretical results, numerical evaluations are performed to emphasize the comparison of DPL and RDPL in the presence and absence of initial stress, as well as the influence of the fractional-order parameter and different times on wave properties. The results show that initial stress has a considerable effect on wave propagation characteristics such as amplitude modulation, propagation speed, and attenuation rate. Furthermore, the use of fractional conformable derivatives and the RDPL formulation allows for more precise modeling and control of the thermal relaxation dynamics. The current study contributes to a better understanding of the linked microelongated and thermal effects in thermoelastic media, as well as significant insights for designing and modeling advanced microscale thermoelastic systems.