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Micro-plate resonators are widely used in sensing and actuation systems.Thermoelastic damping is a significant dominant energy dissipation source.In addition, the size-dependent static and vibration behaviors in microscale structures have been experimentally observed.However, so far we haven t found any reported results that consider the size effect on the thermoelastic damping.In this work, the higher-order governing equations and boundary conditions are derived by using the Hamilton principle.