Thermoelastic damping in micro/nano-plate vibrations: 3D modeling using modified couple stress theory and the Moore–Gibson–Thompson equation

This paper introduces a size-dependent model for evaluating thermoelastic damping (TED) in small-scaled rectangular plates, incorporating three-dimensional (3D) heat transfer. Utilizing the modified couple stress theory (MCST) and Moore–Gibson–Thompson (MGT) heat equation, we enhance the thermomechanical analysis accuracy in micro/nano-structures. The model employs MCST to derive size-dependent constitutive relations for rectangular plates, coupled with the MGT model for formulating the 3D heat conduction equation. This approach facilitates the analysis of the 3D temperature field and aids in defining TED using the energy loss method. Consequently, an analytical expression is developed to predict 3D TED in rectangular plate resonators, integrating characteristic MCST length and nonclassical MGT parameters. Comparative analyses with existing studies and a series of simulated numerical results are presented. These simulations primarily focus on contrasting the 3D model with conventional 1D models and examining the effects of implementing MCST and MGT models. Findings reveal that the proposed formulation significantly alters outcomes for very small and relatively thick plates compared to simpler models. This advancement in modeling provides a more precise understanding of TED in micro/nano-plate structures, offering vital insights for their optimal design and application in advanced technological fields.