TABLE OF CONTENTS Two types of motion sensors, accelerometers and gyroscopes, are needed for detecting the complete motion of a moving object. Accelerometers sense linear motions, and gyroscopes sense angular motions. Traditional mechanical gyroscopes are based on the inertia of a rotating rigid body. New types of gyroscopes have also been developed, e.g. vibratory gyroscopes and optical gyroscopes. For vibratory gyroscopes, the excitation and detection of vibrations can be achieved in electrostatic, piezoelectric or other ways. Recently, using piezoelectric materials to make vibratory gyroscopes has been of increasing interest. Both angular rate induced frequency shifts [65 69] and charge (or current and voltage) [70, 71] in vibrating elastic or piezoelectric structures have been be used to measure angular rates. More references can be found in a review article [72]. This chapter is on the frequency effect. The charge effect will be discussed in the next chapter.
The basic behaviors of a piezoelectric gyroscope can be described by the equations of a rotating piezoelectric body, which consist of the equations of linear piezoelectricity with rotation related Coriolis and centripetal accelerations. A Piezoelectric gyroscope is in small amplitude vibration in a reference frame rotating with it. The equilibrium state in the rotating reference frame is with initial deformations and stresses due to the centrifugal force. Therefore, an exact description of the motion of a piezoelectric gyroscope requires the equations for small, dynamic fields superposed on static initial fields due to the centrifugal force. The governing equations...
