Stochastic and Initial Stress Effects on Wave Propagation in Micro-elongated Thermoelastic Media under the Refined Dual-Phase-Lag Model With Multiplicative White Noise

Abstract

This work provides an in-depth investigation of the influence of initial stress on wave propagation phenomena within a micro elongated stochastic thermoelastic medium with the Lord-Shulman theory (LST), the Dual-Phase-Lag Model (DPLM), and the Refined Dual-Phase-Lag Model (RDPLM). Through an appropriate nondimensionalization procedure combined with a suitable transform technique, the initially complex system of coupled stochastic partial differential equations is systematically transformed into a set of stochastic ordinary differential equations for which explicit analytical solutions can be obtained. The obtained solutions offer a comprehensive understanding of the dynamic response of the medium, including the displacement components, the evolution of micro-elongation, the induced stress fields, and the associated temperature variations. Consequently, the proposed framework delivers a complete and coherent description of thermo-mechanical wave behavior in the presence of initial stress. In addition, extensive numerical simulations are carried out to compare deterministic predictions with their stochastic analogues. These comparisons clearly demonstrate how initial stress effects and random thermal fluctuations significantly modify wave characteristics, such as amplitude, attenuation, and propagation patterns, thereby emphasizing the critical role of stochasticity in realistic thermoelastic wave modeling.