Couple stress-based thermoelastic damping in microrings with rectangular cross section according to Moore–Gibson–Thompson heat equation

It has been confirmed that structures with micro dimensions display size-dependent thermomechanical behaviors. Moreover, according to the findings of empirical and theoretical researches, thermoelastic damping (TED) has been recognized as one of inescapable causes of energy dissipation in microstructures. The current article is an effort to provide a novel size-dependent framework for approximating the amount of TED in microring resonators with rectangular cross section. To include size effect into structural and thermal constitutive relations, the modified couple stress theory (MCST) and the Moore–Gibson–Thompson (MGT) heat equation are utilized, respectively. By solving the coupled heat equation in the purview of MGT model, the fluctuation temperature throughout the ring is determined. By employing the obtained temperature distribution and constitutive relations of MCST, the peak values of strain and wasted thermal energies during one cycle of vibration are computed. Based on the description of TED in the energy dissipation (ED) method, a mathematical expression containing the scale parameters of MCST and MGT model is derived for estimating TED value. To ensure the correctness and veracity of the established solution, a comparative study is carried out on the basis of the data released by other researchers for more plain models. A section is also designated for an all-out study to ascertain the association between TED spectrum and some influential factors like scale parameters of MCST and MGT model, vibration mode number, one-dimensional (1D) and two-dimensional (2D) heat conduction, geometry and material. The extracted data enlighten that the impact of applying MCST and MGT model on TED has a close relationship with the vibration mode number of the ring.