2019
Том 71
№ 6

All Issues

Zatepiakin M. M.

Articles: 3
Letter (Russian)

Correction to the article «On the theory of critical velocities of rotating shafts»

Zatepiakin M. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1963. - 15, № 1. - pp. 116

Brief Communications (Russian)

On the phenomenon of parametric resonance in torsional oscillations of crankshafts

Zatepiakin M. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 403-407

Article (Russian)

On the theory of critical speeds of rotatings hafts

Zatepiakin M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1961. - 13, № 2. - pp. 142-149

Vibrations of a horizontal elastic shaft with a fixed heavy disk on it is described by a system of three nonlinear differential equations of the second order. A. Stodola suggested a particular solution of this system which corresponds to the second critical speed, but a purely theoretical analysis, of the stability of the particular solution suggested by A. Stodola has not been carried out.
An attempt to find a solution of this problem is made in this article. In his analysis the writer uses the method of calculating the logarithm of the monodromy matrix suggested by [5], [7, a], [4].
In our case it enabled us
a)to state the necessary and sufficient conditions of stability,
b)to calculate the zone of stability in the space of parameters.