Developing a Correlation Criterion (SpaceMAC) for Repeated and Pseudo-repeated Modes

摘要

One of the most important factors in the validation of a finite element model is whether the modal vectors obtained from the finite element solution match sufficiently with the modal analysis results of the part or a test prototype. Modal Assurance Criteria (MAC) (Allemang, Brown, A correlation coefficient for modal vector analysis. In: Proceedings of the international modal analysis conference, pp 110-116, 1982) is usually a very effective way to check this condition. However, in case of repeated modal frequencies and vectors, MAC can give misleading results. Hence, there is a need for a method that could indicate how well the finite element method-based estimates for the repeated modes correlate with the modal analysis modes. This work is an attempt to develop a correlation criterion between a set of repeated roots from a finite element method solution and an experimental modal analysis solution. Building on a low dimensional modal vector example, a vector subspace-based approach was identified to help properly define the solution to a characteristic equation with repeated roots. This analogy was extended to higher dimension modal vector cases and vector subspace or hyper planes were identified as a way to model a repeated mode case. Similar to MAC consistency of the solution was considered as ideal way to establish correlation. But in this case the consistency of the solution subspace was found to be more important than that of normalized modal vectors. The smallest principal angle between the two solution subspaces was identified as a way of measuring the consistency. The criterion, referred to as spaceMAC, was developed as a function of this angle such that the range of the criterion is 0-1, similar to MAC was defined as 1-sin(θ) where θ is the principal angle between the two solution subspaces. This criterion was tested with two datasets 2001 Circular Plate Dataset and 2014 Circular Plate Dataset.