Improved Modal Localization and Excitation Factors for Understanding Mistuned Bladed Disk Response

The nodal diameter spectrum is defined based on the discrete Fourier transform of the mode shapes of bladed disks. The dynamic characteristics analysis and assessment for a simplified bladed disk is performed using the concept of the nodal diameter spectrum. For free vibration, the mode localization factor is defined based on the nodal diameter spectrum, and the probabilistic modal properties are obtained for the bladed disk with random mistuning of blade stiffness. For the forced vibration, the modal excitation factor is defined based on the nodal diameter spectrum to evaluate the similarity of engine-order excitation and the mistuned modes. The threshold phenomenon of random mistuning strength and the existence of optimal intentional mistuning are well explained through the combined effects of the modal excitation factor and the corresponding mode localization level of the mistuned mode shape on the response amplitude magnification. The numerical results indicate that the nodal diameter spectrum is an important parameter describing the spatial distributions of the mistuned mode shapes and could be widely applied in the analysis of the dynamic characteristics of mistuned bladed disks.