The influence of the static-pre-stress and mechanical damage variable in the thermal quality factor of two-temperature viscothermoelastic resonators

Hamdy M Youssef,Mohammed W Al-Hazmi

doi:10.1177/1687814020930454

Hamdy M Youssef, Mohammed W Al-Hazmi

Open Access

https://doi.org/10.1177/1687814020930454

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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.

Highlights

The most critical parameter of viscothermoelastic resonators is its thermal quality factor Q
We will develop a mathematical model in which a static-pre-stress and mechanical damage variable will be applied in the context of a two-temperature viscothermoelastic model and resonator of silicon will be considered
The mechanical relaxation time has a significant effect on the thermal quality factor in the context of the one-temperature and two-temperature models

Summary

Introduction

The most critical parameter of viscothermoelastic resonators is its thermal quality factor Q. Experimental results have been utilizing the frequency change to tune resonators These experiments suggest an increase in the Q-factor with the application of tensile stress.[3,28] Youssef constructed a model of thermoelasticity with two-temperature heat conduction equations. This model is based on the conductive temperature and the dynamical temperature. We will develop a mathematical model in which a static-pre-stress and mechanical damage variable will be applied in the context of a two-temperature viscothermoelastic model and resonator of silicon will be considered.

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Conclusion

Declaration of conflicting interests