Size effects of a single delay time parameter on thermoelastic damping in a micro-plate resonator

Despite being at room temperature, thermoelastic damping (TED) plays an important role in energy loss in micro-scale structures. The micro-electro-mechanical system (MEMS) resonators are designed to have low energy dissipation, which is associated with high-quality factors. In couple stress theory, considering the size effect is necessary to explain the problem when plates have micro- or nano-scale thicknesses. This research aims to theoretically obtain an expression for the TED quality factor of size-dependency micro-plate resonators by employing the modified couple stress theory (MCST) with the condition of plane stress and heat conduction for the Quintanilla model. We consider thin silicon micro-plate resonators to explore how the parameter of length scale affects TED’s quality factor. The variation of TED has been examined in terms of the parameters of length-scale, micro-plate thickness, and normalized frequency, and also looked into the impact of phase lag parameters on TED. A comparative study of the proposed model and conventional continuum theory (CCT) has been explained. The present work states that the quality factor of resonators with an infinitesimal thickness may increase by considering small parameter values of phase lags under the modified couple stress theory.