Piezoelectric beams and angular rate sensors

A study of a tuning fork angular rate sensor made out of a single piece of quartz is presented. The piezoelectric effect is used both to excite a reference vibration in the plane of the tuning fork and to detect a vibration normal to this plane. The amplitude of the second vibration is directly proportional to the applied angular velocity. The structure is made rigid in order for it to survive in a harsh environment. This implies that the only vibrationally active areas are the tines of the tuning fork. The performance of the sensor is predicted with the help of a phenomenological piezoelectric beam theory. This theory shows that it suffices to study the two-dimensional dielectric field in the cross-sections of the beams in order to obtain the values of the piezoelectric equivalent components. Estimates of these values can be obtained without the use of special computer programs. The predictions are shown to be in agreement with measurements