Size-dependent analysis of thermoelastic damping in small-scaled circular plates using the Moore-Gibson-Thompson thermoelasticity theory: frequency and energy approaches

Understanding and accurately quantifying thermoelastic damping (TED) in micro/nanoresonators is a major step in designing them to work well. Empirical and theoretical evidence suggests that classical elasticity theory (CET) and the Fourier heat equation break down when applied to structures with minuscule dimensions. This research presents an innovative framework to approximate TED value in miniature circular plates by leveraging both the frequency and energy-based approaches commonly applied in TED studies. The model incorporates the modified couple stress theory (MCST) and Moore-Gibson-Thompson (MGT) heat equation to enhance accuracy beyond the constraints of classical formulation at ultra-small scales. Non-classical constitutive relations and heat equation are firstly derived. Next, the MGT heat conduction equation is solved to determine the temperature distribution within the plate. In conclusion, TED is analytically formulated using two distinct approaches of frequency and energy. The agreement between these two approaches in yielding identical TED expressions reinforces the accuracy of the computations and the credibility of the developed model. The discussion in the numerical results section highlights the influence of essential parameters, especially the characteristic constants of the MCST and MGT model, on TED. The results indicate that while MCST reduces TED and the MGT model increases it, the classical framework, grounded in CET and the Fourier model, predicts a higher TED than the non-classical framework proposed in this study. This suggests that the reduction caused by MCST outweighs the increase due to the MGT model.