Vibration Analysis of Axial Flow Turbine Disks Using Finite Elements

The finite element method is applied to the vibration analysis of axial flow turbine disks. Using the axi-symmetric properties of the configuration of such disks, several finite elements are developed to describe the bending of thin or moderately thick circular plates, and which are characterized by only four- or eight-degrees-of-freedom. These elements incorporate the desired number of diametral nodes in their dynamic deflection functions, and allow for any specified thickness variation in the radial direction. In addition, the effects of in-plane stresses which might arise from rotation or radial temperature gradient, and the effects of transverse shear and rotary inertia in moderately thick plates are readily accounted for. The accuracy and convergence of these elements is demonstrated by numerical comparison with both exact and experimental data for disks.