Effect of Boundary Conditions on Thermoelastic Damping in Microbeam Resonators with Exponentially Varying Thickness

Thermoelastic damping (TED) is a fundamental and dominant energy-dissipation mechanism of micro/nano-resonators operated in vacuum. The quality factor of resonators is limited by TED. Two models, which were proposed by Lifshits and Roukes and Zener, are popularly used to calculate TED values. However, these two models are only suitable for resonators with uniform cross-section, and unsuitable for resonators with non-uniform cross-section. In this work, a numerical model is proposed to compute TED values of non-uniform microbeam resonators with exponentially varying thickness. The effect of constraint boundary conditions including clamped-clamped, clamped-free, free-clamped, and hinged-hinged on thermoelastic damping are investigated. The effectiveness of the present model is verified in comparison with finite-element-method model.