Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness

Ashraf M.  Zenkour; Daoud S.  Mashat

doi:10.4236/am.2010.15057

Ashraf M. Zenkour^*, Daoud S. Mashat

Abstract: In this paper, the analytical and numerical solutions for rotating variable-thickness solid disk and numerical solution for rotating variable-thickness annular disk are presented. The outer edge of the solid disk and the inner and outer edges of the annular disk are considered to have clamped boundary conditions. Two different cases for the radially varying thickness of the solid and annular disks are given. The numerical solution as well as the analytical solution is available for the first case of the solid disk while the analytical solution is not available for the second case of the annular disk. Both analytical and numerical results for displacement and stresses will be investigated for the first case of radially varying thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second case of radially varying thickness is investigated. Finally, the distributions of displacement and stresses will be presented and the appropriate comparisons and discussions are made at the same angular velocity.

Keywords: Rotating, Annular Disk, Solid Disk, Finite Difference Method

Cite this paper: nullA. Zenkour and D. Mashat, "Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness," Applied Mathematics, Vol. 1 No. 5, 2010, pp. 430-437. doi: 10.4236/am.2010.15057.

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