The dynamics of a tuningdisc vibratory gyroscope.
Sedebo, Getachew Temesgen
Sedebo, Getachew Temesgen
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Abstract
Conventional configuration of the discvibratory gyroscope is based on in plane axisymmetric vibrations of the disc with a prescribed circumferential wave number. Due to Bryan’s effect, the vibrating pattern of the disc becomes sensitive to the axial component of inertial rotation of the disc. Rotation of the vibrating pattern relative to the disc is proportional to the inertial angular rate and is measured by sensors. Hence in the conventional configuration, the disc gyroscope is
sensitive to the axial component of the external rotation. In this thesis, an attempt is made to design a single body, discvibratory gyroscope which may replace the conventional three body, disvibratory gyroscope. For this discvibratory gyroscope, both in plane and out-of-plane vibrations (bending vibrations) are excited with different circumferential wave numbers. Inner and outer radii of the disc as well as the disc thickness are matched so that the natural frequencies of the in plane and out-of-plane vibrations coincide, which is the "condition of tuning". In this case the tuning disc gyroscope becomes sensitive to three components of inertial rotation, namely, the axis, the yaxis and the zaxis. Using the theory of linear elasticity and frequency tuning, a formula for the so called "Bryan’s factor" is derived to quantify a shift in angular velocity. In this thesis, analysis of the effects of elastic boundary conditions on the dynamics of thin plate circular discs used as vibratory gyroscope resonators, is performed. The doctoral thesis is also devoted to the investigation of the dynamical aspects of disc vibration and realisation of the conditions of tuning. The thesis also includes the theory of imperfections of the vibratory gyroscope. The solutions to the equations of motion and analysis are presented using computer algebra systems (CASs) such as Mathematica and Maple.
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Submitted in partial fulfillment of the requirements for the degree: Doctor Technologiae: Mathematical Technology in the Department of Mathematics and Statistics, Faculty of Science at the Tshwane University of Technology.
Date
2019-01-05
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Tshwane University of Technology
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Keywords
Gyroscope, Discvibrator, Rotation, Proportional, Circular discs