Modal Scale Factor (MSF)

Modal Scale Factor (MSF) is a factor relating two or more mode shapes used to normalize all mode shapes of the same vibrational mode to a common level for subsequent manipulations.

In case of complex mode shapes, the MSF is a complex number. In case of real mode shapes, the MSF is a real value.

Suppose [ΨA] and [ΨX] are two mode shape estimates (for example [ΨA] is a theoretically-predicted mode shape and [ΨX] is an experimentally-measured mode shape) that you want to compare. The modal scale factor is defined as NOTE:

or

where N is the number of degrees-of-freedom for both A and X data sets, and the superscript * indicates the complex conjugate value.

In the first equation, the mode shape X is the reference to which mode shape A is compared, and in the second equation, mode shape A is the reference.

If the two mode shapes are identical:

[ΨA] = [ΨX],

then

MSF(X,A) = MSF(A,X) = 1

If the two mode shapes differ by a simple scalar multiplier:

[ΨA] = α [ΨX],

then

MSF(A,X) = α

MSF(X,A) = 1/ α

Learn more

Correlation metrics

Pre-test solution process

Correlation solution process

Look up more details

Modal Analysis

Converting complex modes to real modes

Accounting for repeated modes

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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Pre/Post video examples

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Simcenter 3D tutorials

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Modal Scale Factor (MSF), Simcenter 3D 2021.1 Series

© 2020 Siemens

Ewins, D.J., “Modal Testing: Theory, Practice and Application”, Second Edition, Research Studies Press LTD., Baldock, England, 2000.

Allemang, R.J., “The Modal Assurance Criterion — Twenty Years of Use and Abuse”, Sound and Vibration, August 2003.

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