Thermoelastic damping (TED) represents the lower limit of material damping in flexural mode micro- and nanoresonators. Current predictive models of TED calculate damping due to thermoelastic temperature gradients along the beam thickness only. In this work, we develop a two dimensional (2D) model by considering temperature gradients along the thickness and the length of the beam. The Green's function approach is used to solve the coupled heat conduction equation in one and two dimensions. In the 1D model, curvature information is lost and, hence, the effects of structural boundary conditions and mode shapes on TED are not captured. In contrast, the 2D model retains curvature information in the expression for TED and can account for beam end conditions and higher order modes. The differences between the 1D and 2D models are systematically explored over a range of beam aspect ratios, frequencies, boundary conditions, and flexural mode shapes.
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