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Design of Modal Tests

Handbook of Experimental Structural Dynamics

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Abstract

This chapter examines a number of issues that require consideration when a modal test is being planned or designed. As with any engineering procedure, a modal test needs to be designed; otherwise, objectives may not be fulfilled or time and effort may be poorly used. The issues discussed in this chapter include the purpose of the test, excitation considerations, response measurements, support conditions, measurement quality criteria, and considerations for model validation. When a modal test is to be performed to validate a finite element model, one needs to design the test so that the resulting measurements will provide the data required for the correlation of modeling results with those from the test. From a correlation perspective, one would like to select the response locations to allow a definitive, one-to-one correspondence between the measured modes and the predicted modes. Further, the excitation must be designed to excite all the modes of interest at a sufficient level so that the modal estimation algorithms can accurately extract the modal parameters.

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Abbreviations

DOFs:

Degrees of freedom

FFT:

Fast Fourier transform

ω :

Frequency (radian/sec)

FEM:

Finite element model

m :

Mass element of a 2 DOF system

k t :

True stiffness of structure

k s :

Stiffness of the support

c t :

True dam** coefficient

c s :

Dam** coefficient of the support

c m :

Measured dam** coefficient

ω t :

True frequency of structure

ω s :

Frequency due to supports only

ω m :

Measured frequency of structure

ζ t :

True modal dam**

ζ s :

Modal dam** of support system

ζ m :

Measured modal dam**

γ t :

True structural modal dam**

γ s :

Structural dam** of supports

γ m :

Measured structural modal dam**

Δω:

Change in frequency due to support

ϕ j :

value of mass-normalized mode shape at position j

ψ :

Mode shape of interest

C s :

Dam** matrix of support system

TAM:

Test-analysis model

ϕ i :

The ith mass-normalized mode shape

ke ij :

The contribution of the jth DOF to the ith mode generalized mass

KE :

The fractional importance of each FEM DOF to the modal mass

ke i :

Column vector containing contribution of DOF j to the kinetic energy of the ith mode

EfI:

Effective independence sensor selection

y s :

Response at sensor locations

ϕ fs :

Matrix of FEM target mode shapes partitioned to sensor DOFs

q :

Target modal response

w :

The sensor noise

Q :

Fisher information matrix, FIM

G :

A matrix whose columns sum to the eigenvalues of FIM Q

Ψ :

Eigenvectors

λ :

Eigenvalue matrix

F E :

Matrix representing fractional contribution of ith sensor to the jth information matrix eigenvalue

E D :

Effective independence distribution

{1}n:

A column vector of 1’s length n

Min-Mac:

Minimizing MACs-based sensor selection

MAC ij :

Modal assurance criterion between mode shape vectors i and j

φ i :

Mode shape vector for ith mode

Φ :

Mode shape matrix, existing set of sensors

ψ :

Mode shape matrix, remaining set of sensors

a ij :

Elements of A = ΦΤΦ

(MACij)+k:

MAC value between modes i and j with added DOF k

O 12 :

Orthogonality between modes 1 and 2

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Author information

Authors and Affiliations

  1. Sandia National Laboratories, Retired, Albuquerque, NM, USA

    Thomas Carne

  2. ATA Engineering, Inc., San Diego, CA, USA

    Ralph Brillhart & Kevin Napolitano

  3. University of Wisconsin – Madison, Madison, WI, USA

    Daniel Kammer

Authors
  1. Thomas Carne
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  2. Ralph Brillhart
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  3. Daniel Kammer
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  4. Kevin Napolitano
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Corresponding author

Correspondence to Thomas Carne .

Editor information

Editors and Affiliations

  1. University of Cincinnati, Cincinnati, OH, USA

    R. Allemang

  2. Mechanical Engineering, University of Massachusetts Lowell, Lowell, MA, USA

    Peter Avitabile

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Carne, T., Brillhart, R., Kammer, D., Napolitano, K. (2020). Design of Modal Tests. In: Allemang, R., Avitabile, P. (eds) Handbook of Experimental Structural Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6503-8_11-1

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  • DOI: https://doi.org/10.1007/978-1-4939-6503-8_11-1

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  • Print ISBN: 978-1-4939-6503-8

  • Online ISBN: 978-1-4939-6503-8

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Chapter history

  1. Latest

    Design of Modal Tests
    Published:
    18 November 2021

    DOI: https://doi.org/10.1007/978-1-4939-6503-8_11-2

  2. Original

    Design of Modal Tests
    Published:
    23 January 2021

    DOI: https://doi.org/10.1007/978-1-4939-6503-8_11-1

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