An enhanced thermal conduction model for viscous thermal interactions in circular micro-resonators supported by elastic foundations

Abstract

This study investigated the effects of thermoelastic coupling on the viscoelastic behavior of Kelvin-Voigt elastic circular plate resonators. The viscoelastic microsheet resonators were modeled as homogeneous, isotropic structures based on the Winkler foundation. Utilizing the modified Moore-Gibson-Thompson thermoelasticity (MGTE) model, which incorporated both limited thermomechanical diffusion and viscous effects, we solved the governing equations of the proposed system using Laplace transformation methods. Graphical representations of the results were generated using Mathematica software. The study provided detailed discussions that underscored the significant influence of viscosity, the Winkler foundation, and relaxation time on the development of more efficient and effective circular plate structures. Comparisons with previously published studies and results derived from related thermoelastic models were conducted to verify the accuracy of the findings. We found that a stiffer foundation provided stronger support, limiting the extent of deflection under applied loads while also promoting a more uniform temperature distribution in the microplate. Additionally, the viscosity coefficient has a significant impact on the behavior of flexible microplates by reducing temperature distribution, increasing deformation, and amplifying the magnitude of thermal stress. The results enable improved operational accuracy while reducing energy dissipation, making them particularly valuable for high-precision applications.