 | | 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
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| In English (Mech. Solids): | | 4810 |
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| Zhuravlev V.Ph. and Klimov D.M., "Spatial effect of inertness of elastic waves on a sphere," Mech. Solids. 56 (3), 293-295 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
3 |
Pages |
293-295 |
| DOI |
10.3103/S002565442103016X |
| Title |
Spatial effect of inertness of elastic waves on a sphere |
| Author(s) |
Zhuravlev V.Ph. (Institute for Problems of Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia, zhurav@ipmnet.ru)
Klimov D.M. (Institute for Problems of Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia) |
| Abstract |
In 1891, Professor George H. Brian demonstrated the effect of standing wave precession in an elastic axisymmetric shell rotating about an axis of symmetry. To explain the effect, Brian turned to a mathematical description of elastic vibrations of a thin circular ring. As a result, he obtained a formula connecting the constant angular velocity of rotation of the ring in its plane with the speed of precession relative to it of a standing wave of elastic vibrations. Later, this formula was used to explain the effect of rotation of a standing wave in a hemispherical resonator when the resonator itself is rotated around its axis of symmetry. At the same time, the angular rate of rotation was no longer assumed to be constant, and Brian’s ratio between speeds was tacitly extended to the ratio between the angles of rotation. In fact, this meant the discovery of the effect of inertness of elastic waves. In the present study, an already complete spherical resonator is considered, and the plane rotation of the resonator is replaced by a spatial one. The generalized Brian effect is also spatial. |
| Keywords |
Brian effect, angular velocity, spherical resonator |
| Received |
15 October 2020 | Revised |
21 October 2020 | Accepted |
29 October 2020 |
| Link to Fulltext |
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