Abstract
The mechanical damage variable, as well as the thermal and mechanical relaxation times, plays essential roles in the thermal quality factor of the resonators, where controls energy damping through the coupling of mechanical and thermal behavior. In this article, we developed a mathematical model in which a static-pre-stress and mechanical damage variable in the context of a two-temperature viscothermoelasticity of silicon resonator has been considered. The effects of static-pre-stress, thermal relaxation time, mechanical relaxation time, mechanical damage variable, isothermal frequency, and length-scale on the quality factor have been discussed in the context of a one-temperature and two-temperature models. The model predicts that significant improvement in terms of quality factors is possible by tuning the static-pre-stress, isothermal frequency, and length-scale of the resonator. Moreover, the thermal and mechanical relaxation times and the mechanical damage variable have impacts on the thermal quality factor.