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Frequency Response Function Estimation

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Handbook of Experimental Structural Dynamics

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Abstract

For current approaches to experimental modal analysis, the frequency response function is the most important measurement to be made. This chapter develops the frequency response function from the perspective of experimentally measured system excitations and responses. Experimental measurement and numerical processing techniques are presented that allow minimization of the impact of measurement noise and signal processing errors.

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Abbreviations

N :

Number of degrees of freedom

Ni :

Number of inputs

No :

Number of outputs

Ns :

Number of spectral lines (frequencies)

F max :

Maximum frequency (Hz)

ω :

Frequency (rad/s)

Δf :

Frequency resolution (Hz)

T :

Observation period (s)

λ :

Complex eigenvalue

{V }:

Complex eigenvector

[H(s)]:

Transfer function matrix

[H(ω)]:

Frequency response function matrix

{X(ω)}:

Response vector

η :

Noise on response

{F(ω)}:

Excitation vector

υ :

Noise on excitation

[GFF ]:

Input-input power spectral matrix

[GXF ]:

Output-input cross power spectral matrix

[GXX ]:

Output-output power spectral matrix

OCOH :

Ordinary coherence

MCOH :

Multiple coherence

PCOH :

Partial coherence

CCOH :

Cumulative coherence

FCOH :

Fractional coherence

VCOH :

Virtual coherence

SV D :

Singular value decomposition

ED :

Eigenvalue decomposition

CD :

Cholesky decomposition

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Author information

Authors and Affiliations

  1. Structural Dynamics Research Laboratory, Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH, USA

    A. W. Phillips & R. J. Allemang

Authors
  1. A. W. Phillips
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  2. R. J. Allemang
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Corresponding author

Correspondence to A. W. Phillips .

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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Phillips, A.W., Allemang, R.J. (2022). Frequency Response Function Estimation. 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_8

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