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A Unified Development of Basis Reduction Methods for Rotor Blade AnalysisThe axial foreshortening effect plays a key role in rotor blade dynamics, but approximating it accurately in reduced basis models has long posed a difficult problem for analysts. Recently, though, several methods have been shown to be effective in obtaining accurate,reduced basis models for rotor blades. These methods are the axial elongation method,the mixed finite element method, and the nonlinear normal mode method. The main objective of this paper is to demonstrate the close relationships among these methods, which are seemingly disparate at first glance. First, the difficulties inherent in obtaining reduced basis models of rotor blades are illustrated by examining the modal reduction accuracy of several blade analysis formulations. It is shown that classical, displacement-based finite elements are ill-suited for rotor blade analysis because they can't accurately represent the axial strain in modal space, and that this problem may be solved by employing the axial force as a variable in the analysis. It is shown that the mixed finite element method is a convenient means for accomplishing this, and the derivation of a mixed finite element for rotor blade analysis is outlined. A shortcoming of the mixed finite element method is that is that it increases the number of variables in the analysis. It is demonstrated that this problem may be rectified by solving for the axial displacements in terms of the axial forces and the bending displacements. Effectively, this procedure constitutes a generalization of the widely used axial elongation method to blades of arbitrary topology. The procedure is developed first for a single element, and then extended to an arbitrary assemblage of elements of arbitrary type. Finally, it is shown that the generalized axial elongation method is essentially an approximate solution for an invariant manifold that can be used as the basis for a nonlinear normal mode.
Document ID
20010048653
Acquisition Source
Ames Research Center
Document Type
Preprint (Draft being sent to journal)
Authors
Ruzicka, Gene C.
(NASA Ames Research Center Moffett Field, CA United States)
Hodges, Dewey H.
(Georgia Inst. of Tech. Atlanta, GA United States)
Rutkowski, Michael
Date Acquired
August 20, 2013
Publication Date
January 1, 2001
Subject Category
Aerodynamics
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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