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).
Read more about this topic: Vibrating Structure Gyroscope
Famous quotes containing the words theory of, theory and/or operation:
“Hygiene is the corruption of medicine by morality. It is impossible to find a hygienest who does not debase his theory of the healthful with a theory of the virtuous.... The true aim of medicine is not to make men virtuous; it is to safeguard and rescue them from the consequences of their vices.”
—H.L. (Henry Lewis)
“The whole theory of modern education is radically unsound. Fortunately in England, at any rate, education produces no effect whatsoever. If it did, it would prove a serious danger to the upper classes, and probably lead to acts of violence in Grosvenor Square.”
—Oscar Wilde (1854–1900)
“Human knowledge and human power meet in one; for where the cause is not known the effect cannot be produced. Nature to be commanded must be obeyed; and that which in contemplation is as the cause is in operation as the rule.”
—Francis Bacon (1560–1626)