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Practical Techniques for Scaling of Optically Measured Operating Deflection Shapes

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Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8

Abstract

Operational Modal Analysis (OMA) is used to identify vibration patterns of large structures under unknown operating conditions. However, operating data extracted from output-only measurements is not scaled and cannot be used for Structural Dynamic Modification (SDM), frequency response function (FRF) synthesis, force estimation and structural response simulation. Therefore, developing an algorithm that is able to extract scaled mode shapes using measured operating data is desirable. In the current paper, two different scaling techniques including drive point scaling as well as mass sensitivity scaling are employed to scale optically measured operating deflection shapes (ODS). To evaluate the capability of each scaling technique, the scaled optically measured operating shapes are compared to mode shapes extracted using input–output measurements (reference mode shapes). Additionally, the scaled operating shapes are used in structural dynamic modification to demonstrate the benefits and drawbacks associated with the mass sensitivity technique. The results reveal that both mass sensitivity and drive point scaling techniques are capable of effectively scaling optically measured operating deflection shapes of the structure.

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Abbreviations

{Ψ}k1 :

ODS of the unmodified structure

[M1] :

Mass matrix of the unmodified structure

{Ψ}k2 :

ODS of the modified structure

[K1] :

Stiffness matrix of the unmodified structure

[E1] :

Scaled ODS of the unmodified structure

[M2] :

Mass matrix of the modified structure

[E2] :

Scaled ODS of the modified structure

[K2] :

Stiffness matrix of the modified structure

[E un12 ] :

Unscaled mode contribution matrix

[A(s)]:

Residue matrix

[Ẽ2]:

Estimated mode shapes of the modified structure

α k :

Initial scaling factor for unmodified structure

[E12] :

Scaled mode contribution matrix

β k :

Initial scaling factor for modified structure

[Eref] :

Reference shapes extracted using input–output measurement

ω k1 :

Natural frequencies of unmodified structure

pk :

Pole location

ω k2 :

Natural frequencies of modified structure

[ΔM12] :

Mass modification matrix

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Acknowledgements

The authors gratefully appreciate the financial support for this work provided by the Massachusetts Clean Energy Center (CEC), Task Order 13-2. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of Mass CEC.

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Authors and Affiliations

  1. Structural Dynamics and Acoustic Systems Laboratory, University of Massachusetts Lowell, One University Avenue, Lowell, MA, 01854, USA

    Peyman Poozesh, Javad Baqersad, Peter Avitabile & Christopher Niezrecki

  2. Unive Estadual Paulista, Ilha Solteira, SP, Brazil

    Danilo Damasceno Sabino

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  1. Peyman Poozesh
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  2. Danilo Damasceno Sabino
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  3. Javad Baqersad
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  4. Peter Avitabile
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  5. Christopher Niezrecki
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Correspondence to Peyman Poozesh .

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Editors and Affiliations

  1. Mechanical Engineering, Michigan Technological University Mechanical Engineering, Houghton, Michigan, USA

    James De Clerck

  2. Sandia National Laboratory , Albuquerque, USA

    David S. Epp

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Poozesh, P., Sabino, D.D., Baqersad, J., Avitabile, P., Niezrecki, C. (2016). Practical Techniques for Scaling of Optically Measured Operating Deflection Shapes. In: De Clerck, J., Epp, D. (eds) Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-30084-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-30084-9_1

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