A Comparison of Two Reduced Order Methods for Probabilistic Mistuning Investigations

Slight variances in the manufacturing of rotating machinery can lead to significant changes in the structural dynamic behavior compared to the behavior of ideal cyclic periodic structures. Therefore it is necessary to consider deviations from the perfect cyclic periodic structures in the mechanical design process of rotating machinery. To minimize the effort of numerical calculations, the application of reduced order models is indispensable. The objective of this paper is the comparison of two reduction methods which are not widespread in application of rotationally periodic structures. For the validation of the implemented methods, a generic model of a thin plate meshed with shell elements and a representative large size FE model of a radial turbine wheel are used. The first reduction method is called Improved Reduced System and is based on the classical Guyan reduction. The second reduction method is called SEREP method and is from a theoretical point of view closely related to the first method although the procedure to obtain the reduction basis is quite different. The results show for both test cases an excellent agreement between the reduced order models and the unreduced finite element model. Both reduction methods are also able to capture the phenomena of mode localization. It is also found that through the application of the reduced order methods the computation time can be reduced by two orders of magnitude. Based on the first reduction method, the statistical mistuning behavior is studied using the accelerated Monte Carlo simulation.