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Finite Element Model Correlation

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Handbook of Experimental Structural Dynamics

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Abstract

Correlation of a finite element model with test data is commonly performed. In order to perform these correlation studies, the finite element model may require reduction due to the large size of the model, or the test data may be expanded to the size of the finite element model. Model reduction and model expansion techniques are presented first. Correlation tools typically deployed are then presented. Some additional commentary related to the test data and the correlation process is also provided to give insight into some of the issues that must be faced.

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Abbreviations

FEM:

Finite element model

EMA:

Experimental modal analysis

SEREP:

System equivalent reduction expansion process

IRS:

Improved reduced system

MAC:

Modal assurance criteria

CoMAC:

Coordinate modal assurance criteria

POC:

Pseudo orthogonality check

CORTHOG:

Coordinate orthogonality check

FRAC:

Frequency response assurance criteria

RVAC:

Response vector assurance criteria

MACCO:

Modal assurance criteria contribution

FRF:

Frequency response function

DOF:

Degree of freedom

NDOF:

Full set of “n” finite element DOF

ADOF:

Reduced set of “a” test DOF

DDOF:

Remaining set of “d” deleted or omitted DOF

[M]:

Analytical mass matrix

[C]:

Analytical damping matrix

[K]:

Analytical stiffness matrix

[U]:

Analytical modal matrix

[I]:

Diagonal modal mass matrix

[Ω2]:

Diagonal modal stiffness matrix

[T]:

Transformation matrix

[E]:

Experimental modal vectors

[D]:

Dynamic matrix

{ẍ}:

Acceleration

{ẋ}:

Velocity

{x}:

Displacement

{F}:

Force

{p}:

Modal displacement

{u}:

Modal vector

{ei}:

ith experimental modal vector

{uj}:

jth analytical modal vector

ek:

kth degree of freedom of the experimental modal vector

up:

pth degree of freedom of the analytical modal vector

n:

Full set of finite element DOF

a:

Tested set of experimental DOF (also master/active DOF)

d:

Deleted (omitted) set of DOF

S:

Static condensation

I:

IRS condensation

f:

Dynamic condensation

U:

SEREP condensation

H:

Hybrid condensation

k,p:

Degree of freedom identifiers

i,j:

Mode identifiers

T:

Transpose

g:

Generalized inverse

−1:

Standard inverse

*:

Conjugate

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Author information

Authors and Affiliations

  1. Structural Dynamics and Acoustic Systems Laboratory, University of Massachusetts Lowell, Lowell, MA, USA

    Peter Avitabile

  2. University of Cincinnati, Cincinnati, OH, USA

    Michael Mains

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  1. Peter Avitabile
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Correspondence to Peter Avitabile .

Editor information

Editors and Affiliations

  1. Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH, USA

    Randall Allemang

  2. Structural Dynamics and Acoustic Systems Laboratory, University of Massachusetts Lowell, Lowell, MA, USA

    Peter Avitabile

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Avitabile, P., Mains, M. (2022). Finite Element Model Correlation. In: Allemang, R., Avitabile, P. (eds) Handbook of Experimental Structural Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4547-0_17

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