From ControlTheoryPro.com

Contents
1 Introduction to MEMS Gyro Modeling
See Also 

MEMS gyroscopes rely on two principles. The first principle is the resonating vibration of the proof mass. The second principle is the Coriolis effect.
2 Mechanical Resonator^{[1]}
The amplitude of a mechanical resonator can be described with the following equation
'Amplitude of Vibration' 
The properties are as follows
 is the frequency of vibration,
 is the time scale over which the amplitude decays due to energy losses, and
 is the quality factor.
There are reasons for designing a MEMS gyro with a high Q
 higher gain
 narrow frequency response
 lower energy loss per cycle
Therefore high Q leads to higher performance MEMS devices.
Modeling of the MEMS gyro principles is key to designing
 the geometry
 the chosen materials
 the resonant frequency
The Q is a result of these properties.
3 ThermoElastic Damping^{[2]}
Anyone who has dealt with MEMS gyros has come across the fact that they are temperature sensitive. One engineer suggested that what you really bought was a thermometer that happened to put out a rate too.
Mechanical engineers are familiar with the idea that a material stiffness changes with temperature. The hotter a metal gets the softer it gets. On a MEMS scale where the mechanism is extremely small. Coupling of stress, strain, and temperature become a means for energy loss. This is referred to as Thermoelastic Damping (TED).
The reference material provides a detailed set of equations and examples.
4 Resources
 Mohite, S., Patil, N., Pratap, R., "Design, modeling and simulation of vibratory micromachined gyroscopes.", Journal of Physics: Conference Series 34 (2006), pp. 757763.
 Thermoelastic Damping and Engineering for High Q MEMS Resonators
 Boa, M. 2004 Micro Mechanical Transducers. 2nd. Elsevier. ISBN 044450558X
 Gaura, E., and Newman, R 2006 Smart MEMS and Sensor Systems. 1st. Imperial College Press. ISBN 1860944930