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

Abstract

This study conducts a comprehensive investigation of stochastic effects on wave propagation in a micro-elongated thermoelastic medium within the frameworks of the Lord–Shulman theory (LST), the Dual-Phase-Lag model (DPLM), and the Refined Dual-Phase Lag model (RDPLM). Through the application of an appropriate nondimensionalization procedure combined with an effective transform technique, the initially complex system of coupled stochastic partial differential equations is systematically reduced to a set of stochastic ordinary differential equations, from which explicit analytical solutions are obtained. The derived solutions offer valuable insight into the dynamic response of the medium, including displacement components, micro-elongation evolution, stress fields, and temperature variations. Consequently, the proposed formulation provides a unified and self-consistent framework for describing thermo-mechanical wave propagation. In addition, extensive numerical simulations are carried out to compare deterministic results with their stochastic counterparts. These comparisons demonstrate that random thermal disturbances significantly influence key wave characteristics, such as amplitude, attenuation, and propagation behavior, underscoring the crucial role of stochasticity in realistic thermoelastic wave modeling