An Eigenvalue Analysis for Calculating the Vibrational Modes of Steam Turbine Discs

Abstract

Summary This paper describes the application of numerical procedures to an engineering design problem of considerable practical importance. The problem is that of calculating the natural frequencies of vibration of steam turbine discs. The analysis is based on a variational formulation in conjunction with finite difference procedures to transform the problem to an eigenvalue problem. This is characterized by a symmetric band matrix, and the vibrational frequencies which correspond to the eigenvalues are computed using standard eigenvalue programming packages. The analysis includes a description of both natural and forced boundary conditions for the problem. An essential feature of this investigation is the relative simplicity in elasticity theory used and the associated computational procedures. As such it should be of interest to teachers of final year engineering mathematics courses and to mechanical engineering students embarking on an M.Sc. programme. From a research standpoint, the paper offers the p...