Dmytro М. Lila^*, А. А. Martynyuk

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Cherkasy National Bohdan Khmelnytsky University, Cherkasy, Ukraine.
Stability of Processes Department, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine.
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Abstract: 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.

Keywords: Axisymmetric Elastoplastic Problem; Method of Boundary Shape Perturbation; Rotating Inhomogeneous Circular Disc; Stability Loss; Failure of Bearing Capacity; Critical Angular Velocity

Cite this paper: D. Lila and А. Martynyuk, "Analysis of Dynamics of Boundary Shape Perturbation of a Rotating Elastoplastic Radially Inhomogeneous Plane Circular Disk: Analytical Approach," Applied Mathematics, Vol. 3 No. 5, 2012, pp. 451-456. doi: 10.4236/am.2012.35068.

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