  A semi-analytical study of the acoustic radiation losses associated with
various transverse vibration modes of a micromechanical (MEMS) annular
resonator is presented. The quality factor, Q, of such resonators is of
interest in many applications and depends on structural geometry, interaction
with the external environment, and the encapsulation method. Resonators with at
least one surface exposed to air can display losses through acoustic radiation
even at micro meter dimensions. Published experimental results suggest the
dominance of acoustic losses in the Q of a MEMS drum resonator. In this study,
a well established mathematical techniques to analytically model resonator
vibration modes and fluid-structure interaction are used, and a semi-analytical
procedure for computing Q due to acoustic radiation losses, Qac, in any
vibrational mode outlined. Present technique includes calculation of the exact
mode shape and its utilization in computing Qac. The dependence of Qac on the
first 15 mode shapes is computed. Results are compared for the lowest 2 modes
of a solid circular resonator using exact mode shapes to those of Lamb's
approximate mode shapes. Comparison to published experimental results validates
the predictive utility of the technique, especially for higher modes where
acoustic radiation seems to be the dominant constituent of Q.
