The second approximation in a small parameter to the solution of the problem of loss of the stability of a rotating disk in the refined formulation

Authors

  • D.M. Lila Bohdan Khmelnytsky National University of Cherkasy

DOI:

https://doi.org/10.15407/dopovidi2018.07.033

Keywords:

boundary shape perturbation method, critical angular velocity, elastoplastic problem, rotating disc, stability loss

Abstract

We have proposed a way of the investigation of the possible loss of stability by a rotating thin circular disk by the method of small parameter. We have obtained a characteristic equation for the critical radius of plastic zone in the second approximation in a small parameter on the basis of Saint-Venant's yield condition. We also have found the critical angular rotational velocity.

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References

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Guz', A. N. & Nemish, Yu. N. (1989). Method of Perturbation of the Shape of the Boundary in Continuum Mechanics. Kyiv: Vyshcha Shkola (in Russian).

Lila, D. M. (2018). The second approximation in the small parameter to the solution of the problem of the elastoplastic instability of a rotating disk. Dopov. Nac. akad. nauk Ukr., No. 5, pp. 36-43(in Russian). doi: https://doi.org/10.15407/dopovidi2018.05.036

Lila, D. M. (2017). On the method of perturbations in the problem of elastoplastic instability of a rotating disk. Dopov. Nac. akad. nauk Ukr., No. 9, pp. 48-54 (in Russian). doi: https://doi.org/10.15407/dopovidi2017.09.048

Lila, D. M. & Martynyuk, A. A. (2011). About the stability loss of a rotating elastoplastic circular disc. Dopov. Nac. akad. nauk Ukr., No. 1, pp. 44-51 (in Russian).

Lila, D. M. (2011). Eccentric form of stability loss of a rotating elastoplastic disk. Dopov. Nac. akad. nauk Ukr., No. 2, pp. 49-53 (in Russian).

Lila, D. M. & Martynyuk, A. A. (2012). Development of instability in a rotating elastoplastic annular disk. Int. Appl. Mech., 48, No. 2, pp. 224-233. doi: https://doi.org/10.1007/s10778-012-0518-x

Lila, D. M. (2016). Elastoplastic instability of thin rotating disk. Appl. Probl. Mech. and Math., No. 14, pp. 92-98 (in Russian).

Published

15.05.2024

How to Cite

Lila, D. (2024). The second approximation in a small parameter to the solution of the problem of loss of the stability of a rotating disk in the refined formulation . Reports of the National Academy of Sciences of Ukraine, (7), 33–39. https://doi.org/10.15407/dopovidi2018.07.033