Analytical Solutions To Variable Thickness and Variable Material Property Rotating Disks for a New Three-Parameter Variation Function

Abstract

Analytical solutions of two different annular rotating disk problems are obtained under the assumptions of plane stress, isotropy, and small deformations. The first problem involves a homogeneous variable profile disk, whereas the second one is a functionally graded disk having a variation in elasticity modulus. For the variations of disk thickness and elasticity modulus in these problems, a new form of nonlinear function controlled by three parameters is introduced. The derivations of the closed form solutions for both type of rotating disk problems are carried out in a unified form. The closed form solutions are verified numerically by the nonlinear shooting method.