Determination of resonant frequencies of axisymmetric oscillationsof a hollow ball using of the equations of motionof three-dimensional elasticity theory

Vestnik MGSU 7/2015
  • Bobyleva Tat’yana Nikolaevna - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 25-32

A great number of works have been written on the frequencies of spherical bodies. In construction hollow balls are widely used. For this reason it is important to investigate the dynamics of such bodies, in particular, their resonance oscillations. In the paper we obtained an equation for determining the resonant frequencies of axisymmetric oscillations of a hollow ball. The general solution of three-dimensional equation of motion is used in a spherical coordinate system. Frequency equations of purely radial oscillations of solid and hollow balls are given as special cases. These equations coincide with those obtained previously. The solution may be used in boundary problems for arbitrary loaded space bodies, all the three dimensions of which are relatively equal, in the dynamic tasks for high-frequency oscillations.

DOI: 10.22227/1997-0935.2015.7.25-32

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