Vibrations of a Rotating Piezoelectric Body and Applications in Gyroscopes
Huiyu Fang, Ph.D. Candidate - Defense of Doctoral Dissertation
Department of Engineering Mechanics
University of Nebraska - Lincoln
Advisors: Dr. Jiashi Yang and Dr. Qing Jiang
Date: Monday, June 5, 2000
Time: 9:30 a.m.
Place: W196 Nebraska Hall
Piezoelectric materials can be used to make gyroscopes (rotation sensors) to measure the angular rate of a rotating body. Piezoelectric gyroscopes are resonant devices. They detect angular rate either through rotation-induced change of vibration frequency (wave speed), or rotation-induced electric signals (charge, current, or voltage). The behavior of piezoelectric gyroscopes can be described by the linear theory of piezoelectricity in a rotating reference frame. For the development, modeling and design of piezoelectric gyroscopes, analyses of a few basic problems of the vibration of a rotating piezoelectric body are performed. Thickness vibrations and propagating waves in an infinite piezoelectric plate rotating at a constant angular rate about its normal and waves propagating over a rotating piezoelectric half-space are analyzed using the three-dimensional equations. Rotation sensitivity (rotation-induced frequency shift) is calculated. The dependence of the rotation sensitivity on a few physical and geometric parameters is examined. To model piezoelectric gyroscopes operating with the vibration modes of finite piezoelectric bodies, zero-dimensional equations for a piezoelectric parallelepiped, one-dimensional equations for a piezoelectric ring, and one-dimensional equations for a piezoelectric beam bimorph are developed. These structural equations, and the two-dimensional equations of piezoelectric shells, are used to analyze a ceramic plate gyroscope, a quartz plate gyroscope, a ceramic beam bimorph gyroscope, a ceramic ring gyroscope, and a ceramic shell gyroscope. These gyroscopes detect rotation rate by electrical signals. Voltage (and/or current) sensitivity is calculated. The dependence of the sensitivity on various parameters is studied.
