A Model for Thermoelastic Damping in Microplates

We present a model and analytical expressions for the quality factors of microplates due to thermoelastic damping. We solve the heat equation for the thermal current across the thickness of a microplate, and hence decouple the thermal equation from the plate equation. We utilize a perturbation method to derive an analyt-ical expression for the quality factor of microplates, of general boundary conditions under electrostatic loading and residual stresses, in terms of their structural mode shapes. For the special case of no electrostatic and in-plane loadings, we derive a simple analytical expression for the quality factor, which is independent of the mode shapes. We verify the model by comparing the calcu-lated quality factors of the special case of microbeams to theoretical results obtained using the microbeam models in the literature. We present several results for various modes of microplates with various boundary conditions