Thermoelastic damping analysis for size-dependent microplate resonators utilizing the modified couple stress theory and the three-phase-lag heat conduction model

Abstract

Thermoelastic damping (TED) is considered to be a factor of significant energy loss in micro-scale structures, even at room temperature. The prediction of TED is therefore very important in the designing of micro-electro-mechanical system (MEMS) resonators with high-quality factors. When the thickness of the beams and plates are at microscale or nanoscale, the size-effect is needed to be considered. Couple stress theory is developed as a size-dependent continuum theory to deal with such problems. In the present work, an analytical expression for the quality factor (Q) of TED for size-dependent microplate resonators is derived by applying the modified couple stress theory (MCST) considering plane stress condition and the three-phase-lag (TPL) heat conduction model. We consider Kirchhoff microplate resonators and as case study, the effect of the length-scale parameter on the quality factor of TED are discussed in detail. To study the behavior of TED, the material of the microplate resonator is considered to be Silicon. The variations of TED as functions of the normalized frequency, microplate thickness, and length-scale parameter have been investigated. The effect of phase-lag parameters on TED has also been discussed. The results of the present model are compared to the existing results of the classical continuum theory. The present work investigates that the modified couple stress theory with small values of phase-lag parameters can increase the quality factor of microplate resonators with a smaller thickness.