微谐振器纵向振动热弹性耦合分析

对微谐振器在纵向振动时的热弹性耦合进行分析，以悬臂梁为基础，在环境温度为300 K时，对热弹性本构方程进行数值求解，对在纵向振动过程中产生的温度、受热弹性耦合的影响产生的频率漂移、热弹性阻尼进行分析.分析结果发现，在纵向振动过程中，悬臂梁在前3阶振动模态下，温度变化量随着振动模态的升高而增大，在3阶振动模态时，温度变化量约为1.5 K；受热弹性耦合影响，频率漂移比首先随着梁长的增加而迅速增加，然后稳定在1.67×10-4附近；热弹性阻尼最大值约为1.0×10-4.然后，使用COMSOL Multiphysics软件对悬臂梁进行热弹性耦合仿真，并对数值结果进行验证.结果表明，仿真结果与理论计算结果相吻合. 

Analysis on Thermoelastic Damping of Micro Resonators from Longitudinal Vibration

The thermoelastic coupling of micro resonators from the longitudinal vibration mode was analyzed. And constitutive equations of thermoelastic coupling were deduced based on the cantilever beam at the surrounding temperature of 300 K. The temperature resulted from longitudinal vibration, the frequency shift ratio and thermoelastic damping were analyzed. The results demonstrate that in the process of the first three longitudinal vibrations, the temperature vibration increases with the vibration modes. And in the third mode, the temperature vibration is about 1.5 K. The frequency shift ratio sharply increases with the beam length firstly, and then the curve gradually approaches the horizontal line at a fixed value close to 1.67×10^-4. Peak value of thermoelastic damping is about 1.0×10^-4. At last, the COMSOL multiphysics was used to simulate the thermoelastic coupling of the cantilever beam to verify the numerical results. The results show that the simulation results are coincided with the theoretical results.