 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| G.T. Sedebo, M.Y. Shatalov, S.V. Joubert, M.C. Kekana, A.A. Shafi, and T. Alhaji, "Theory of Imperfections of Three-Dimensional Tuning Plate Gyroscope. Part I: Material Imperfections," Mech. Solids. 58 (4), 1395-1409 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
4 |
Pages |
1395-1409 |
| DOI |
10.3103/S0025654423600939 |
| Title |
Theory of Imperfections of Three-Dimensional Tuning Plate Gyroscope. Part I: Material Imperfections |
| Author(s) |
G.T. Sedebo (Tshwane University of Technology, Pretoria, 0183 South Africa; Department of Mathematics and Statistics, Pretoria, 0183 South Africa, sedebogt@tut.ac.za)
M.Y. Shatalov (Tshwane University of Technology, Pretoria, 0183 South Africa; Department of Mathematics and Statistics, Pretoria, 0183 South Africa, shatalovm@tut.ac.za)
S.V. Joubert (Tshwane University of Technology, Pretoria, 0183 South Africa; Department of Mathematics and Statistics, Pretoria, 0183 South Africa, joubertsv@tut.ac.za)
M.C. Kekana (Tshwane University of Technology, Pretoria, 0183 South Africa; Department of Mathematics and Statistics, Pretoria, 0183 South Africa, kekanamc@tut.ac.za)
A.A. Shafi (Tshwane University of Technology, Pretoria, 0183 South Africa; Department of Industrial Engineering, Pretoria, 0183 South Africa, ajutinaa47@gmail.com)
T. Alhaji (Tshwane University of Technology, Pretoria, 0183 South Africa; Department of Mathematics and Statistics, Pretoria, 0183 South Africa, sirtikass66@gmail.com) |
| Abstract |
Imperfections resulting from fabrication processes are the major sources of limitation of the performance of disc vibratory gyroscopes/sensors. The presence of imperfections in these sensors causes deviations from ideal mass, stiffness, Poisson’s ratio, and non-homogeneity of damping distributions in the material and the surrounding medium. The damping imperfection is considered in terms of a viscous damping model. Natural frequency mismatch and localized mode shapes are the most common and easily observable consequences of imperfections in a resonator designed to operate in a degenerate mode. It is essential to understand the nature of sensors and control the sensors that are subjected to various forms of imperfections. Sensor fabrication involves various steps and each step contributes to imperfections. In practice, imperfections are reflected in asymmetry and aniso-elasticity, thereby resulting in undesirable perturbations. In this paper we considered the influence of imperfections on the accuracy of a 3D (three-dimensional) tuning plate gyroscope. This paper mainly focuses on the imperfections resulting from materials that are used to manufacture the sensor. For the purpose of this paper, all effects of imperfections discussed are considered in terms of a linear model. Nonlinear considerations will be dealt with in subsequent papers. We considered a solid disc or plate gyroscope to model our sensor. The system vibrates both in- and out-of-plane with circumferential wave numbers m and n=m+1, respectively. We derive the equations of motion for a system where imperfections are taken into account. Based on linear approximations we used the 2mth harmonics of the imperfections for the in-plane mode and the 2(m+1)st harmonics of the imperfections for the out-of-plane mode. In addition to linear approximations, we further assumed that the in- and out-of-plane effects of imperfections are independent and hence can be separated. |
| Keywords |
vibratory disc gyroscope, three-dimensional, geometric imperfections, linear approximation, tuning, averaging, bryan's factor |
| Received |
05 June 2023 | Revised |
09 June 2023 | Accepted |
10 June 2023 |
| Link to Fulltext |
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