Thermoelastic damping of micro resonators operating in the longitudinal vibration mode: In comparison with the case of flexural vibration

• Derive a simple formula of thermoelastic damping for longitudinal vibration.
• The formula is verified by comparing with exact solutions.
• It is shown that Landau–Lifshitz's model overestimates thermoelastic damping.
• Comparison of thermoelastic damping in longitudinal vibration and flexural vibration.

This paper studies thermoelastic damping in the longitudinal vibration mode. Expression of thermoelastic damping is obtained by using the thermal-energy method and is then validated by comparing with the exact solutions deduced from the coupled thermoelasticity equations. It is demonstrated that Landau–Lifshitz's model overestimates thermoelastic energy loss by employing the adiabatic assumption. Results of the present study indicate that the peak value of thermoelastic damping for isothermal boundary condition is lower than that for adiabatic boundary condition in the longitudinal vibration mode. Furthermore, a comparison was made between longitudinal vibration mode and flexural vibration mode to distinguish their different characteristics. It manifests that thermoelastic damping of rods or beams reaches peak values at the length scale of 10−8 m for longitudinal vibration in contrast to the order of 10−5 m or above for flexural vibration in the numerical examples of the present study.