Abstract：An analytical model for thermoelastic damping is presented for micromechanical resonators with coupling effect between bending and torsion. The static and dynamic equations are utilized to solve structure deflections in coupled motion of torsion and bending. The bending component of the coupled motion causes thermoelastic damping. However, both torsion and bending motions are taken into consideration to calculate energy stored, which is different from other models without torsion component. A simple analytical expression of thermoelastic damping is derived by using the heat conduction equation and LR theory. The present model is validated by comparing its results with the finite-element method solutions. The thermoelastic damping obtained by the present model is compared to the measured internal friction of single paddle oscillators. It is found that thermoelastic damping contributes significantly to internal friction for the case of high-order modes. The effects of structure dimensions on thermoelastic damping are explored.
2014, Vol. 33 
