A. M. Zenkour and D. S. Mashat, “Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness,” Applied Mathematics, Vol. 1, No. 5, 2010, pp. 431-438.

has been cited by the following article:

• TITLE: Stability Loss of Rotating Elastoplastic Discs of the Specific Form

  AUTHORS: Dmitrii Makarovich Lila, Anatolii Andreevich Martynyuk

  KEYWORDS: Axisymmetric Elastoplastic Problem, Boundary Shape Perturbation Method, Rotating Circular Annular Disc, Stepped Disc, Stability Loss, Critical Angular Velocity

  JOURNAL NAME: Applied Mathematics, Vol.2 No.5, May 6, 2011

  ABSTRACT: A method of calculating a possible stability loss by a rotating circular annular disc of variable thickness is suggested within the theory of perfect plasticity with the help of small parameter method. A characteristic equation for a critical radius of a plastic zone is obtained as a first approximation. The formula for the critical angular velocity, determining the stability loss of the disc according to the self-balanced form, is derived. The method using which we can take into account the disc’s geometry and loading parameters is also specified. The efficiency of the proposed method is shown in Section 5 while considering an illustrative example. The values of critical angular velocity of rotating are found numerically for different parameters of the disc.