Wave Propagation in a Fiber-Reinforced Visco-Thermoelastic Medium with Voids under the Influence of Nonlocal and Memory-Dependent Derivatives using Lord-Shulman Theory

Abstract

<title>Abstract</title> This research investigates how thermoelastic waves travel through a fiber-reinforced, viscous-thermoelastic material that contains voids. It considers the impact of both nonlocal interactions and memory-dependent derivatives on this wave propagation. The material model was built within the framework of the Lord–Shulman theory, which introduces a thermal relaxation time to overcome the limitations associated with classical thermoelasticity theories. The resulting system of partial differential equations was transformed using appropriate dimensionless variables, which helped generalize the analysis and simplify the study of the effects of physical parameters. The analytical solution was derived using the normal mode analysis method. This technique simplified the model into an algebraic system, enabling a thorough investigation of the wave's properties. The effects of fiber reinforcement, viscosity, and non-locality were illustrated through theoretical representation and graphical plots. The results provide deeper insight into the dynamic behavior of fiber-reinforced composite materials under coupled thermal and mechanical effects.