 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 57, Issue 6 / 2022 | Next article >> |
| G.T. Sedebo, M.Y. Shatalov, S.V. Joubert, and A.A. Shafi, "The Dynamics of a Three-Dimensional Tuning Functionally Graded Plate Gyroscope," Mech. Solids. 57 (6), 1577-1589 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
6 |
Pages |
1577-1589 |
| DOI |
10.3103/S0025654422060267 |
| Title |
The Dynamics of a Three-Dimensional Tuning Functionally Graded Plate Gyroscope |
| 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)
A.A. Shafi (Tshwane University of Technology, Pretoria, 0183 South Africa; Department of Industrial Engineering, Pretoria, 0183 South Africa, ajutinaa47@gmail.com) |
| Abstract |
Gyroscopes operating along a single axis are widely developed and are currently batch-fabricated. Several applications which require three-dimensional (3D) motion have necessitated the need for a detailed study of a 3D vibratory gyroscope. We consider a functionally graded plate gyroscope (FGPG) with an arbitrary number of sections supported by means of a rigid stem at the center. The system vibrates both in- and out-of-plane. We derive the equations of motion for the system and show that a slow 3D inertial rotation rate of the gyroscope can be calculated approximately in terms of amplitudes of vibration. These amplitudes should be experimentally determinable. The in- and outof-plane vibrations are excited respectively with different circumferential wave numbers. To realise a 3D vibrational gyroscope, the in- and out-of-plane eigenvalues are tuned by means of the variation of radial and/or axial lengths. To better understand the ordinary differential equations (ODE’s) modeling this system, we introduced an averaging operator. Numerical examples are included for two concentric components of the FGPG, where the inner component is made from an aluminum alloy and the outer component is made from a titanium alloy. Frequency spectra diagrams of tuned in- and out-of-plane vibrations are plotted. Diagrams of normalised eigenfunctions for both in- and out-of-plane vibrations are plotted. |
| Keywords |
functionally graded plate gyroscope, three-dimensional, tuning, averaging, force-to-rebalance, frequency spectra |
| Received |
18 August 2022 | Revised |
09 September 2022 | Accepted |
16 September 2022 |
| Link to Fulltext |
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