On the method of perturbations in the problem of elastoplastic instability of a rotating disk
DOI:
https://doi.org/10.15407/dopovidi2017.09.048Keywords:
boundary shape perturbation method, critical angular velocity, elastoplastic problem, rotating disc, stability lossAbstract
In the study of the loss of stability by a rapidly rotating thin circular disk, a possible form of perturbation of the initial contour circle is elucidated. The first four approximations are obtained for the small parameter of the linearized boundary conditions and the conjugation conditions for the solutions.
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Ivlev, D. D. (2002). Mechanics of Plastic Media, Vol. 2: General Problems. Rigid-Plastic and Elastoplastic State of Bodies. Hardening. Deformation Theories. Complex Media. Moscow: Fizmatlit (in Russian).
Guz', A. N. & Nemish, Yu. N. (1989). Method of Perturbation of the Shape of the Boundary in Continuum Mechanics, Kyiv: Vyshcha Shkola (in Russian).
Ivlev, D. D. & Ershov, L. V. (1978). Perturbation Method in the Theory of Elastoplastic Bodies, Moscow: Nauka (in Russian).
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).
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