Thermoelastic Damping in the Size-Dependent Microplate Resonators Based on Modified Couple Stress Theory

The dynamic properties and behaviors of microplate resonators have been experimentally shown to be size dependent. The thermoelastic damping plays an important role on the inherent energy dissipation of the microplate resonators. Based on the modified couple stress theory, the size-dependent thermoelastic damping in microplate resonators is investigated. The governing equation of motion is derived by using Hamilton principle. The thermoelastic damping is obtained via solving the heat diffusion equation. The presented results of thermoelastic frequencies have a good agreement with the reported values. The result shows that the size effect has significant impact on the thermoelastic damping when the plate thickness has a similar value to the material length scale parameter. It demonstrates that the thermoelastic damping can be suppressed and the quality factor can be enlarged as the material length scale parameter increases. The quality factor is improved by several orders of magnitude as the representative temperature drops from 500 to 80 K. However, the size-dependent quality factor at 400 K is larger than that at 293 K when the thickness of the plate has a similar value of the material length scale parameter. In addition, the differences among different plate materials are small, as the plate thickness is less than the characteristic thickness. However, those gaps become larger when the characteristic thickness is overtaken.