Thermoelastic dissipation of hollow micromechanical resonators

This paper studies the effects of hollow geometry on thermoelastic dissipation of tubular beam resonators of circular cross-section. Quality factor Q is calculated for hollow tubes at size scale ranging from millimeter to nanometer with different surface thermal conditions (including adiabatic, isothermal or a mixed surface condition). It is found that hollow geometry of tubular resonators has a surprising frequency-dependent effect on the quality factor Q, which can change the Q factor by almost two orders of magnitude as compared to a solid circular beam of same outer diameter. In particular, the hollow geometry effect on the Q factor is opposite for high or low frequencies, and the effect of isothermal surface condition is almost one order of magnitude stronger than that of adiabatic surface condition especially for hollow tubes of thinner wall-thickness. The present analysis suggests that, to achieve a higher quality factor, hollow tubular resonators with isothermal surface condition are best to operate at low frequencies, while hollow tubular resonators with adiabatic surface condition are best to operate at high frequency. For a doubly clamped thin-walled tubular resonator vibrating at its lower natural frequencies, the present results suggest that adiabatic surface thermal condition is favorable at millimeter scale while isothermal surface condition is favorable at nanometer scale.