Stochastic Finite Element Analysis for High Speed Rotors

Abstract

The general problem of the dynamic response of highspeed rotors is considered in which certain system parameters may have a spatial stochastic variation. In particular the elastic modulus and mass density of a rotating shaft are described through one dimensional stochastic field functions so that the imperfections in manufacture and measurement can be accounted for. The stochastic finite element method is developed so that the variability of the response of the rotor can be interpreted in terms of the variation of the material property. As an illustration the whirl speed analysis is performed to determine the stochastics of whirl speeds and modes through the solution of a random eigenvalue problem associated with a non self-adjoint system. Numerical results are also presented.