Vibratory angular rate gyroscope using polarized piezoceramic bimorphs.

摘要

This dissertation analytically models the dynamic characteristics of a vibratory angular rate gyroscope composed of microscopic piezoceramic bimorphs arranged in the shape of two back-to-back tuning forks using a linear elastoelectricity variational principle.; Due to the complicated nature of the sensor system proposed in this research, simpler systems are first analyzed as an aid in making assumptions. Analyses on models for a simpler two-degree of freedom and a cantilever-beam vibratory angular rate gyroscopes provide insight into the understanding and the development of more realistic, albeit more complicated, structures involved in the proposed system using bimorphs constructed with piezoceramics for extended rotating rate range.; Two types of vibratory gyroscopes with bimorphs are analyzed: tuning fork shaped vibratory gyroscopes composed of two cross-jointed bimorph plates, one connected with a base beam and the other to an annular sector plate. A modified Hamilton's principle with the two-dimensional plate theory, for both out-of-plane and in-plane motions of rectangular and annular sector plate, is utilized to develop a new analytical method using dispersion relations with mixed-boundary conditions. The Timoshenko beam theory for the base beam is also employed. Tiersten's method involving the expansion of electric potential is developed for the two-dimensional bimorph plate theory, which, with further reduction of the coupled differential equations, yields coupled constitutive equations for the thin bimorph plate with the degenerate differential equations of electric potential components.; The resulting analytical models are evaluated numerically at the fundamental flexural mode frequency. The proposed systems for the analysis represent one half of a single tuning fork shape; use of mirror symmetries of that basic shape allows the construction of an H-shaped tuning fork gyroscope. The dimensions of such an H-shaped MEMS device are approximately 150μm x 40μm x 4μm with fundamental natural frequencies ranging between 200–300 kHz for half of a tuning fork shape.; The necessity of having simultaneously large amplitudes in the actuating and sensing directions results in a greater sensitivity and allows the two forced vibration problems to be successfully solved only at the matched first natural frequency with the fundamental flexural mode obtained from the eigenanalysis through variations of the geometry.