弯扭耦合影响的MEMS扭转谐振器件中的热弹性阻尼

Thermoelastic damping in MEMS torsion resonators in consideration of coupling effect between torsion and bending

热弹性阻尼作为一种基本的能量耗散机理,对高质量因数的MEMS谐振器件有着重要的影响。因为纯扭转振动不产生热弹性能量耗散,所以过去很少有文献涉及到扭转器件中热弹性阻尼。但是,静电驱动的扭转谐振器件中通常存在弯扭耦合现象,其中弯曲振动的部分不可避免的产生热弹性阻尼。针对具有弯扭耦合的MEMS扭转谐振器件,给出一种热弹性阻尼解析模型。首先考虑弯扭耦合效应,利用MEMS扭转谐振器件的静态平衡方程和动力学方程,得到线性振动方程,然后根据热传导方程和LR理论推导出热弹性阻尼的解析模型。将解析模型与FEM仿真结果及实验数据比较,证实了理论的可行性并揭示了热弹性阻尼在内部耗散中的重要性。通过对解析模型特性的研究,分析了谐振器件几何尺寸对热弹性阻尼的影响关系。

An analytical model of thermoelastic damping was presented for micromechanical resonators considering the coupling effect between bending and torsion.The static and dynamic equations were built 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 were taken into consideration to calculate the energy stored,which is different from other models without consideration of torsion component.A simple analytical expression of thermoelastic damping was derived by using the heat conduction equation and LR theory.The presented model was validated by comparing its results with the finite-element method solutions.The thermoelastic damping obtained by the presented model was compared to the measured internal friction of a single paddle oscillator.It is found that thermoelastic damping contributes significantly to internal friction in the case of high-order modes.The effects of structure dimensions on thermoelastic damping were explored.