Stochastic finite element analysis for high speed rotors
Abstract
A general finite element method is developed for the dynamic analysis of complex rotor systems in which several of the system parameters are stochastic quantitites. The stochastic characteristics of the free and forced vibration response are derived in terms of the stochastic material property characteristics. An equation is developed in which the variations of the modulus of elasticity and the mass density along the length of the shaft are represented as small fluctuations about their mean values and in terms of two independent, one dimensional, univariate real stochastic fields which are homogeneous with zero mean values. These are described through their variances and autocorrelation function. The Lagrangian equations of motion for the element when the system is rotating at a constant velocity are derived. The equation of motion of free vibration are reduced to the eigenvalue problem. Each stochastic process is characterized by three parameters: the mean, standard deviation, and scale of fluctuation so that the second order properties can be adequately extracted. The local average of any stochastic process and the cross covariances between any two stiffness coefficients or any two mass coefficients can be derived. The stochastic properties of the solution of the eigenvalue problem are determined by the perturbation method.
 Publication:

13th Canadian Congress of Applied Mechanics
 Pub Date:
 May 1991
 Bibcode:
 1991ccam.proc..610S
 Keywords:

 Dynamic Structural Analysis;
 EulerLagrange Equation;
 Finite Element Method;
 Forced Vibration;
 Free Vibration;
 Rotors;
 Stochastic Processes;
 Mean;
 Modulus Of Elasticity;
 Standard Deviation;
 Stiffness;
 Variance;
 Mechanical Engineering