|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|
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|
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