Accounting for repeated modes

Symmetric structures exhibit repeated modes that have almost identical natural frequencies. The symmetry can be either cyclic or with respect to one or more axes. Each test or reference mode shape can be rotated around the axis of symmetry by a different angle, with respect to the equivalent analysis or work mode shape. Therefore, it is not sufficient to rotate one of the models. To account for repeated modes of the symmetric structures, a method is provided that operates on clusters of test and analysis repeated modes.NOTE

The mode pairing software expresses the test (reference) modes as a linear combination of the analysis (work) modes within the same modal subspace or cluster as follows:

[T]=[A]✕[W]+[R]

where:

• [T] is the matrix of the test modes in the modal subspace.

• [A] is the matrix of the analysis modes in the same modal subspace.

• [W] is the matrix of the unknown weighting factor. These are the coordinates of the test modes in the analysis modal subspace basis.

• [R] is the residual term.

If the modal subspaces are completely coinciding, then the residual term [R] is zero. If the residual [R] is too big, the two modal subspaces will not match.

The weighting factors can be computed as follows:

[W]=[A]-1✕[T]

The equivalent transformed analysis modes [Aeq] can then be computed as the linear combination of the original analysis modes that approximates the test modes as follows:

[Aeq]=[A]✕[W]

The original analysis or work modes in the cluster are then replaced with new transformed work modes.

If the process results in a high value of the residual error, approximately 100%, the likely reasons are:

• Improper cluster definition.

• Poor node mapping.

• Incorrect transformation of the mode shapes between analysis and test coordinate systems.

• Poor quality test modes.

Learn more

Pre-test solution process

Correlation solution process

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Modal Analysis

Converting complex modes to real modes

Modal Scale Factor (MSF)

Modal Assurance Criteria (MAC)

Coordinate MAC (COMAC)

Cross-orthogonality (X-Ortho)

Frequency Response Assurance Criterion (FRAC)

Min-MAC algorithm

MODMAC algorithm

Normal Mode Indicator Function (NMIF) algorithm

Driving Point Residue algorithm

Scientific literature references for correlation

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Accounting for repeated modes, Simcenter 3D 2021.1 Series

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F. Lembregts, Modal correlation for axisymmetric models with repeated roots – wheel rim case study, ISMA 2016 - International Conference on Noise and Vibration Engineering. B. Franca de Paula, G. Rejdych, T. Chancelier, G. Vermot Des Roches, E. Balmes, On the Influence of Geometry Updating on modal correlation of brake components, XVIII symposium Vibrations, Shocks & Noise (VISHNO) 2012.

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