Dynamic Systems Theory Analysis of the Probabilistic Thermo-Viscoelastic Response of a Composite Plate Using the Rayleigh-Ritz Method

Abstract: This paper presents a probabilistic investigation into the thermo-viscoelastic response of a composite plate under a parabolic temperature distribution, employing the Rayleigh-Ritz method within the framework of Dynamic Systems Theory. The analysis meticulously examines the time-dependent interplay between material behavior and thermal effects, crucial for advanced engineering applications. Our approach integrates time-dependent relaxation moduli and thermal expansion coefficients into a comprehensive model to capture the dynamic characteristics of the plate. A detailed formulation of the system's potential energy, incorporating both elastic strain energy and thermal work, is presented. We utilize trigonometric Ritz functions to approximate the stress and displacement fields. This approach captures the coupled thermo-mechanical and viscoelastic response of the plate with particular attention to the impact of the thermal expansion and time-dependent stresses. We determine the unknown coefficients of the Ritz functions via a minimization process, allowing for a precise approximation of the system. This probabilistic approach is essential for understanding how variations in temperature, time, and material parameters affect the structural integrity of the plate. This study provides a thorough understanding of the dynamic response of composite plates under time-varying thermal and mechanical loading.