Angular rate sensors

A vibrating structure angular rate sensor 100 comprises a substrate 114; a plurality of supporting structures 204 fixed to the substrate 114; an annular member 202 flexibly supported by the plurality of supporting structures 204; a drive system arranged to apply a periodic driving force such that the annular member 202 oscillates, in use, in a primary mode of vibration at a resonant frequency f 1 , with an amplitude of motion that generates a restoring force from the plurality of supporting structures 204; and a pick-off system arranged to determine the amplitude of motion of a secondary mode of vibration at a resonant frequency f 2 , in which oscillation of the annular member 202 is induced by the Coriolis force resulting from an angular rate experienced by the sensor 100. In use, the restoring force has a non-linear relationship with the amplitude of motion and a number p of supporting structures 204 is selected such that f 1 =f 2 .