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.
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REFERENCES
G. H. Bryan, “On the beats in the vibrations of revolving cylinder or bell,” Proc. Cambr. Phil. Soc. 7, 101–107 (1981).
W. B. Scott, “Delco makes low-cost gyro prototype,” Aviat. Week. 117 (17), 64–72 (1982).
E. J. Loper and D. D. Lynch, “The HRG: A new low-nose inertial rotation sensor,” in Proc. 16th Jt. Services Data Exchange for Inertial Systems. Los Angeles, Calif., 16–18 Nov 1982 (Los Angeles, 1982), pp. 432–433.
V. Ph. Zhuravlev and D. M. Klimov, “Dynamic effects in an elastic rotating ring,” Izv. Akad Nauk SSSR. Mekh. Tverd. Tela, No. 5, 17–23 (1983).
V. Ph. Zhuravlev and D. M. Klimov, Wave Solid-State Gyroscope (Nauka, Moscow, 1985) [in Russian].
V. S. Chernina, “Natural vibrations of a thin closed spherical shell,” in Theory of Shells and Plates (Nauka, Moscow, 1973), pp. 575–579.
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The study was supported by a grant from the Russian Science Foundation (project no. АААА-А20-120011690132-4).
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Translated by I. K. Katuev
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Zhuravlev, V.P., Klimov, D.M. SPATIAL EFFECT OF INERTNESS OF ELASTIC WAVES ON A SPHERE. Mech. Solids 56, 293–295 (2021). https://doi.org/10.3103/S002565442103016X
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DOI: https://doi.org/10.3103/S002565442103016X