Analytical Solutions for Rotating Exponentially-graded Annular Disks With Various Boundary Conditions

This paper presents accurate elastic solutions for rotating annular disks. A new material properties and density profile in exponential form containing four geometric parameters is proposed. Analytical solutions using this profile are obtained in terms of Whittaker's functions for the elastic deformation of rotating annular disks. The inner and outer edges of the disk are considered to have combinations of clamped and free boundary conditions. Special cases of rotating annular disks are investigated, which include annular disks with constant thickness and constant density, exponentially variable elastic properties and density, and exponentially graded disks. For all cases studied, closed form solutions are obtained and numerical results are presented. The results include the radial displacement, circumferential and radial stresses of the four annular disk configurations for combinations of homogeneous and exponentially graded cases. The distributions of stresses and displacement are obtained and comparisons between different cases are made at the same angular velocity.