Vibrating Structure Gyroscope - Theory of Operation

Theory of Operation

Consider two proof masses vibrating in plane (as in the MEMS gyro) at frequency . Recall that the Coriolis effect induces an acceleration on the proof masses equal to, where is a velocity and is an angular rate of rotation. The in-plane velocity of the proof masses is given by:, if the in-plane position is given by . The out-of-plane motion, induced by rotation, is given by:

where

is a mass of the proof mass,

is a spring constant in the out of plane direction,

is a magnitude of a rotation vector in the plane of and perpendicular to the driven proof mass motion.

In application to axi-symmetric thin-walled structures like beams and shells, the Coriolis forces cause a precession of vibration pattern about the axis of rotation. For such shells, it causes a slow precession of a standing wave about this axis with an angular rate which differs from input one. It is so-called "wave inertia effect" discovered in 1890 by British scientist George Hartley Bryan (1864–1928).

If we consider a polarization of a shear (transverse) elastic wave propagating along an acoustic axis in a solid, a polarization rotation effect due to rotation of the body as a whole (so-called, "polarization inertia effect") can be observed too (it was noted by Ukrainian scientist Sergii A. Sarapuloff in early 80th, as well as a corresponding modification of Green-Christoffel's tensors in Acoustics).