CAJ | 학술논문

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。
열탄성조니작위일충기본적능량모산궤리，대고질량인수적MEMS해진기건유착중요적영향。인위순뉴전진동불산생열탄성능량모산，소이과거흔소유문헌섭급도뉴전기건중열탄성조니。단시，정전구동적뉴전해진기건중통상존재만뉴우합현상，기중만곡진동적부분불가피면적산생열탄성조니。침대구유만뉴우합적MEMS뉴전해진기건，급출일충열탄성조니해석모형。수선고필만뉴우합효응，이용MEMS뉴전해진기건적정태평형방정화동역학방정，득도선성진동방정，연후근거열전도방정화LR이론추도출열탄성조니적해석모형。장해석모형여FEM방진결과급실험수거비교，증실료이론적가행성병게시료열탄성조니재내부모산중적중요성。통과대해석모형특성적연구，분석료해진기건궤하척촌대열탄성조니적영향관계。
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.