Study of Thermo-Viscoelastic Interactions in Microplates Resting on an Elastic Foundation and Subjected to External Loads Using DPL Thermoelastic Model

Abstract

This work specifically examines the modeling of the transient thermodynamic reaction of a Kirchhoff–Love thermoelastic thin circular plate that is simply supported and set on an elastic base of Winkler type. The plate experiences a time-varying external load. The Kelvin-Voigt model is employed to simulate the viscoelastic behavior of the plate in this investigation. The modified dual-phase-lag (DPL) thermoelasticity model is used to represent the intricate thermoelastic properties of the plate accurately. The DPL thermoelastic model includes the effects of restricted thermomechanical diffusion, which considers the connection between thermal and mechanical events in the plate. This model offers a more extensive depiction of the plate's reaction, considering both temperature and mechanical factors. Analytical solutions for the studied variables, such as deflection, temperature, displacement, bending moment, and thermal stress, were extracted using the Laplace transform. The viscoelastic coefficient, Winkler base, and the angular frequency of the distributed load greatly affect how circular plate structures behave, as shown by numerical examples and insightful discussions. Finally, to verify the validity of the results and the proposed model, they were compared with previously published studies and their corresponding thermoelastic models.