Component-mode-based reduced order modeling techniques for mistimed bladed disks - Part I: Theoretical models

Component mode synthesis (CMS) techniques are widely used for dynamic analyses of complex structures. Significant computational savings can be achieved by using CMS, since a modal analysis is performed on each component structure (substructure). Mistuned bladed disks are a class of structures for which CMS is well suited. In the context of blade mistuning, it is convenient to view the blades as individual components, while the entire disk may be treated as a single component. Individual blade mistuning may then be incorporated into the CMS model in a straightforward manner. In this paper, the Craig-Bampton (CB) method of CMS is formulated specifically for mistuned bladed disks, using a cyclic disk description. Then a novel secondary modal analysis reduction technique (SMART) is presented: a secondary modal analysis is performed on a CB model, yielding significant further reduction in model size. In addition, a straightforward non-CMS method is developed in which the blade mistuning is projected onto the tuned system modes. Though similar approaches have been reported previously, here it is generalized to a form that is more useful in practical applications. The theoretical models are discussed and compared from both computational and practical perspectives. It is concluded that using SMART, based on a CB model, has tremendous potential for highly efficient, accurate modeling of the vibration of mistuned bladed disks.