Open AccessAnalysis of Dynamics of Boundary Shape Perturbation of a Rotating Elastoplastic Radially Inhomogeneous Plane Circular Disk: Analytical Approach
Author(s) -
Д. М. Лила,
A. À. Martynyuk
Publication year - 2012
Publication title -
applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2152-7393
pISSN - 2152-7385
DOI - 10.4236/am.2012.35068
Subject(s) - angular velocity , physics , perturbation (astronomy) , rotation (mathematics) , radius , mechanics , dynamics (music) , boundary value problem , mathematical analysis , critical ionization velocity , classical mechanics , critical radius , mathematics , geometry , spheres , computer security , quantum mechanics , computer science , astronomy , acoustics
For a rotating inhomogeneous circular disk a way of calculating dynamics of boundary shape perturbation and failure of bearing capacity is proposed in terms of small parameter method. Characteristic equation of plastic zone critical radius is obtained as a first approximation. A formula of critical angular velocity is derived which determines the stability loss of the disc according to the self-balanced form. Efficiency of the proposed method is shown by an illustrative example considered in Section 7. Values of critical angular velocity of rotation are found numerically for different parameters of the disc