Mechanics of Solids (about journal) Mechanics of Solids
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in January 1966
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IssuesArchive of Issues2002-6pp.70-76

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Yu. G. Markov and I. V. Skorobogatykh, "The determination of the vibration frequency of a nonhomogeneous rotating axisymmetric body," Mech. Solids. 37 (6), 70-76 (2002)
Year 2002 Volume 37 Number 6 Pages 70-76
Title The determination of the vibration frequency of a nonhomogeneous rotating axisymmetric body
Author(s) Yu. G. Markov (Moscow)
I. V. Skorobogatykh (Moscow)
Abstract The influence of the deviations from an ideal scheme due to nonhomogeneous density of the material on the dynamics of an axisymmetric elastic body is studied. The distribution of the density is assumed to depend on the angle. The case of variable density is important for practice, since the density distribution can be controlled. We consider three cases. In the first case, the terms with the angular velocity are much greater than the terms accounting for the nonhomogeneity. The second case is the opposite of the first case. In the third case, all terms have the same order of magnitude. It is shown that nonhomogeneity of the material gives rise to frequency splitting, i.e., two close different frequencies appear instead of two equal frequencies. This effect leads to beating-type phenomena. It is established that a change in the density with respect to a fixed harmonic affects only certain vibration modes. Similar issues are considered in [2].
1.  V. Ph. Zhuravlev and D. M. Klimov, Hemispherical Resonator Gyro [in Russian], Nauka, Moscow, 1985.
2.  Yu. G. Markov and I. V. Skorobogatykh, "On vibrations of a rotating viscoelastic axisymmetric body under the action of a surface load," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 72-80, 1995.
3.  S. P. Timoshenko, D. H. Young, and W. Weaver, Vibration Problems in Engineering [Russian translation], Mashinostroenie, Moscow, 1985.
4.  V. Ph. Zhuravlev and D. M. Klimov, Applied Methods in the Theory of Oscillations [in Russian], Nauka, Moscow, 1988.
Received 8 May 2001
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