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.