The loss of stability of a rotating resilent plastic plane disk with decreasing radius

1Lila, DM, 2Martynyuk, AA
1Bohdan Khmelnytsky National University of Cherkasy
2S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2014, 2:56-62
https://doi.org/10.15407/dopovidi2014.02.056
Section: Mechanics
Language: Russian
Abstract: 

The dependence of the critical speed of rotation on the variable radius of a contour circle is determined by means of the small parameter method. Proceeding from the Saint-Venant condition of fluidity, we obtain the characteristic equation for the critical radius of a plastic zone in the first approximation. The values of the critical angular speed of rotation for various parameters of the system are determined numerically.

Keywords: loss of stability, resilient plastic plane disk
References: 

1. Ivlev D. D. Izv. AN USSR. OTN, 1957, No. 1: 141–144 (in Russian).
2. Ershov L. V., Ivlev D. D. Izv. AN USSR. OTN, 1958, No. 1: 124-125 (in Russian).
3. Ivlev D. D., Ershov L. V. The perturbation method in the theory of an elastoplastic body. Moscow: Nauka, 1978 (in Russian).
4. Guz A. N., Nemish Yu. N. Method of perturbation of the shape of the boundary in the mechanics of continuous media. Kyiv: Vyshcha shkola, 1989 (in Russian).
5. Guz A. N., Babich I. Yu. Three-dimensional theory of stability of deformable bodies. Kyiv: Nauk. dumka, 1985 (in Russian).
6. Sokolovsky V. V. Theory of plasticity. Moscow: Vyshaia shkola, 1969 (in Russian).
7. Bitsenko K. B., Grammel R. Technical Dynamics. Vol. 2. Moscow; Leningrad: GITTL, 1952 (in Russian).
8. Bitsenko K. B., Grammel R. Technical Dynamics. Vol. 1. Moscow; Leningrad: GITTL, 1950 (in Russian).
9. Lila D. M., Martynyuk A. A. Dopov. Nac. akad. nauk Ukr., 2011, No. 1: 44–51 (in Russian).
10. Lila D. M. Dopov. Nac. akad. nauk Ukr., 2011, No. 2: 49–53 (in Russian).
11. Lila D. M., Martynyuk A. A. Int. Appl. Mech., 2012, 48, No. 2: 224–233. https://doi.org/10.1007/s10778-012-0518-x