Modeling and simulations of thermoelastic damping in microplates

We present a model and analytical expressions for the quality factors of microplates of general shapes and boundary conditions due to thermoelastic damping. We solve the heat equation for the thermal flow across the microplate, and hence decouple the thermal equation from the plate equation. We utilize a perturbation method to derive an analytical expression for the quality factor of a microplate under electrostatic loading and residual stresses in terms of its 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 specializing it to a microbeam and comparing the resulting quality factor to that obtained using microbeam models in the literature. We present several results for various modes of rectangular microplates with various boundary conditions.