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Prediction of Forced Response on Ancillary Subsystem Components Attached to Reduced Linear Systems

  • Conference paper
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Dynamics of Coupled Structures, Volume 1

Abstract

Multi-component structural systems are commonly used in the modeling of dynamic systems. In order to simplify such complex mathematical models, peripheral/ancillary components are often times grouped as larger substructures of the total assembly. The dynamic response of the structural system will have the embedded characteristics of the appended ancillary components but the fidelity of the model will be highly dependent on the quality and resolution of the model. In particular, sufficient substructure information is needed for an accurate prediction of the response of the appendage and/or its coupling structure. This implies that proper characterization of the structure may require measurements at the subcomponent level or in the absence of sufficient data, a large and detailed finite element model.

In this work, analytical models of a multi-component beam system were created to investigate the prediction of the dynamic response of ancillary subcomponents. The ancillary structure will be assumed to be dynamically active but inaccessible/immeasurable. The models will be created first at full space as a reference and then reduction techniques will be used to determine the necessary information in order to accurately predict the force or displacement imparted to the appendages. The dynamic characteristics of the ancillary component will be extracted using the subcomponent information available from the system.

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Abbreviations

{Xn}:

Full set displacement vector

{Xa}:

Reduced set displacement vector

{Xd}:

Deleted set displacement vector

[Ma]:

Reduced mass matrix

[Mn]:

Expanded mass matrix

[Ka]:

Reduced stiffness matrix

[Kn]:

Expanded stiffness matrix

[Ua]:

Reduced set shape matrix

[Un]:

Full set shape matrix

[Ua]g :

Generalized inverse

[T]:

Transformation matrix

[TU]:

SEREP transformation matrix

{p}:

Modal displacement vector

[M]:

Physical mass matrix

[C]:

Physical damping matrix

[K]:

Physical stiffness matrix

{F}:

Physical force vector

\( \left\{\ddot{\mathrm{x}}\right\} \) :

Physical acceleration vector

\( \left\{\dot{\mathrm{x}}\right\} \) :

Physical velocity vector

{x}:

Physical displacement vector

α:

Parameter for Newmark integration

β:

Parameter for Newmark integration

Δt:

Time step

[U12]:

Mode contribution matrix

ADOF:

Reduced degrees of freedom

DOF:

Degrees of freedom

ERMT:

Equivalent reduced model technique

FEM:

Finite element model

MAC:

Modal assurance criterion

NDOF:

Full space degrees of freedom

SEREP:

System equivalent reduction expansion process

TRAC:

Time response assurance criterion

References

  1. Thibault L (2012) Development of equivalent reduced model technique for linear modal components interconnected with nonlinear connection elements. Master’s Thesis, University of Massachusetts Lowell

    Google Scholar 

  2. Marinone T (2012) Efficient computational nonlinear dynamic analysis using modal modification response technique. Master’s Thesis, University of Massachusetts Lowell

    Google Scholar 

  3. Marinone T, Thibault L, Avitabile P (2013) Expansion of nonlinear system response using linear transformation matrices from reduced component model representations. Proceedings of the thirty-first international modal analysis conference, Garden Grove, CA, Feb 2013

    Google Scholar 

  4. Pingle P, Niezrecki C, Avitabile P (2011) Full field numerical stress-strain from dynamic experimental measured data. EURODYN 2011, Leuven, Belgium, July 2011

    Google Scholar 

  5. Avitabile P, Harvie J (2013) Reduced order system model nonlinear response and expansion for full field results. Eleventh international conference on recent advances in structural dynamics, Pisa, Italy, July 2013

    Google Scholar 

  6. Avitabile P (2003) Twenty years of structural dynamic modification – a review. Sound and Vibration Magazine, pp 14–27

    Google Scholar 

  7. Thibault L, Avitabile P, Foley J, Wolfson J (2012) Equivalent reduced model technique development for nonlinear system dynamic response. Proceedings of the thirtieth international modal analysis conference, Jacksonville, FL, Feb 2012

    Google Scholar 

  8. Guyan RJ (1965) Reduction of stiffness and mass matrices. AIAA J 3(2):380

    Article  Google Scholar 

  9. O’Callahan JC (1989) A procedure for an improved reduced system (IRS) model. Proceedings of the seventh international modal analysis conference, Las Vegas, NV, Feb 1989

    Google Scholar 

  10. O’Callahan JC, Avitabile P, Riemer R (1989) System equivalent reduction expansion process. Proceedings of the seventh international modal analysis conference, Las Vegas, NV, Feb 1989

    Google Scholar 

  11. Nonis C, Avitabile P (2013) System model modes developed from expansion of uncoupled component dynamic data. Eleventh international conference on recent advances in structural dynamics, Pisa, Italy, July 2013

    Google Scholar 

  12. Marinone T, Butland A, Avitabile P (2012) A reduced model approximation approach using model updating methodologies. Conference proceedings of the society for experimental mechanics series 2012, Topics in modal analysis II, vol 6, pp 625–636

    Google Scholar 

  13. Newmark NM (1959) A method of computation for structural dynamics. J Eng Mech Div ASCE 85(3):67–94

    Google Scholar 

  14. Allemang RJ, Brown DL (2007) A correlation coefficient for modal vector analysis. Proceedings of the first international modal analysis conference, Orlando, FL, Feb 2007

    Google Scholar 

  15. Van Zandt T (2006) Development of efficient reduced models for multi-body dynamics simulations of helicopter wing missile configurations. Master’s Thesis, University of Massachusetts Lowell

    Google Scholar 

  16. MAT_SAP/MATRIX (1986) A general linear algebra operation program for matrix analysis. Dr. John O’Callahan, University of Massachusetts Lowell

    Google Scholar 

  17. MATLAB R2010a. The MathWorks, Natick, MA 2010

    Google Scholar 

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Acknowledgements

Some of the work presented herein was partially funded by Air Force Research Laboratory Award No. FA8651-10-1-0009 “Development of Dynamic Response Modeling Techniques for Linear Modal Components”. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the particular funding agency. The authors are grateful for the support obtained.

Author information

Authors and Affiliations

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

    Sergio E. Obando & Peter Avitabile

Authors
  1. Sergio E. Obando
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  2. Peter Avitabile
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Corresponding author

Correspondence to Sergio E. Obando .

Editor information

Editors and Affiliations

  1. Engineering Physics Department, University of Wisconsin Madison, Madison, Wisconsin, USA

    Matt Allen

  2. Sandia National Laboratories, Albuquerque, New Mexico, USA

    Randy Mayes

  3. Lehrstuhl fur Angewandte Mechanik, Technische Universitat Munchen, Garching, Germany

    Daniel Rixen

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© 2014 The Society for Experimental Mechanics, Inc.

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Obando, S.E., Avitabile, P. (2014). Prediction of Forced Response on Ancillary Subsystem Components Attached to Reduced Linear Systems. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04501-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-04501-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04500-9

  • Online ISBN: 978-3-319-04501-6

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