Abstract
This paper presents the analytical and numerical solutions for a rotating variable-thickness solid disk. The outer edge of the solid disk is considered to have free boundary conditions. The governing equation is derived from the basic equations of the rotating solid disk and it is solved analytically or numerically using finite difference algorithm. Both analytical and numerical results for the distributions of stress function and stresses of variable-thickness solid disks are obtained. Finally, the distributions of stress function and stresses are presented and the appropriate comparisons and discussions are made at the same angular velocity.
Highlights
The theoretical and experimental investigations on the rotating solid disks have been widespread attention due to the great practical importance in mechanical engineering
As the effect of thickness variation of rotating solid disks can be taken into account in their equation of motion, the theory of the variable-thickness solid disks can give good results as that of uniform-thickness disks as long as they meet the assumption of plane stress
It is to be noted that the parameter n determines the thickness at the outer edge of the solid disk relative to h0 while the parameter k determine the shape of the profile
Summary
The theoretical and experimental investigations on the rotating solid disks have been widespread attention due to the great practical importance in mechanical engineering. Most of the research works are concentrated on the analytical solutions of rotating isotropic disks with simple cross-section geometries of uniform thickness and variable thickness. Zenkour and Allam [8] have developed analytical solution for the analysis of deformation and stresses in elastic rotating viscoelastic solid and annular disks with arbitrary crosssections of continuously variable thickness. As many rotating components in use have complex cross-sectional geometries, they cannot be dealt with using the existing analytical methods. Zenkour and Mashat [12] have presented both analytical and numerical solutions for the analysis of deformation and stresses in elastic rotating disks with arbitrary cross-sections of continuously variable thickness. The analytical solution for rotating solid disk with arbitrary cross-section of continuously variable thickness is presented. A number of application examples are given to demonstrate the validity of the proposed method
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