A Mathematical Analysis of Thermoelastic Characteristics of a Rotating Circular Disk with an FGM Coating at the Outer Surface

Abstract

A thin circular rotating disk having a concentric hole and a functionally graded material (FGM) coating at the outer surface is considered with a view to analyzing the thermoelastic characteristics due to a thermal load and rotation of the disk. The FGM coating is assumed to have exponentially varying Young's modulus, coefficient of thermal expansion (CTE), and density in the radial direction of the disk. The Poisson's ratio is assumed to be constant throughout the disk. The incompatible eigenstrain developed in the disk owing to the nonuniform CTE and variation of temperature is taken into consideration. Using the two-dimensional thermoelastic theories, the two-dimensional plane stress axisymmetric problem is formulated as a second order differential equation. A finite element model is developed using the variational approach and Ritz method to obtain the numerical solution of the differential equation. The validity of the finite element model is justified for a rotating circular disk of homogeneous material by comparing the finite element results with analytical solution obtained by Timoshenko. Then the finite element model is applied to the problem of an Al disk with an Al2O3/Al FGM coating at its outer surface. The numerical results of the thermoelastic field demonstrate that the temperature distribution profile, angular speed of the disk, and FGM coating thickness are the crucial factors to be considered in controlling the thermoelastic characteristics of a rotating disk with an FGM coating.