Use of the finite element method for the vibration analysis of rotating machinery

The finite element method has been used to predict the effect of rotation on the vibrational characteristics of structures. Kinematics of rotary motion were studied and numerical adaptation for the calculation of the acceleration matrices has been accomplished. Successful computation of the eigenvalue equation was achieved and a solution algorithm based on a modified QL method was then used. Existing three dimensional isoparametric finite elements were modified to add the extra acceleration matrices. Comparison with existing methods shows a very good agreement, typical discrepancies being 1-2%. It was shown that the centrifugal loading creates an initial stress field the effect of which can incorporated by the introduction of a geometric stiffness matrix. While the initial stresses are the largest contributors to the changes in the natural frequencies, they had only a very small effect on the mode shapes of any of the structures that were examined. The centripetal accelerations were found to have a smaller influence on the natural frequencies. It was found that the natural frequences changed with the angular speed according to the Southwell equation. The effect of the Coriolis acceleration on the natural frequencies is negligibly small. The mode shapes of rotating structures are affected by the Coriolis acceleration component and for some structures this effect is significant