Analysis of thermoelastic dissipation in couple stress-based beams with two-dimensional Moore–Gibson–Thompson heat conduction

Thermoelastic dissipation (TED) is a primary source of energy loss in extremely small structures, making the precise determination of its magnitude vital for the optimal design and performance of such components. The inclusion of two-dimensional (2D) heat conduction alongside size effects in both the structural and thermal domains plays a key role in enhancing TED analysis for small-scale beam resonators. The modified couple stress theory (MCST) and Moore–Gibson–Thompson (MGT) heat equation, within the context of the energy approach, are employed in this paper to create a novel size-dependent framework for TED in small-scale beams subjected to 2D heat conduction. After comparing the developed framework with existing research, numerical simulations are carried out to reveal the differences between 2 and 1D models, as well as the impact of employing size-dependent mechanical and thermal formulations. For beams with large thickness-to-length ratios, especially under clamped–clamped (CC) boundary conditions, the proposed model shows significant differences when compared to 1D model. Based on the findings, the ratio of 2D TED to 1D TED in CC beams with an aspect ratio of 10 can be up to 1.6 times. The integration of size effects and 2D heat transfer in the established framework is expected to provide benchmark results for accurate TED simulations and facilitate the optimal design of ultra-small beam resonators.