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Towards Dynamic Substructuring Using Measured Impulse Response Functions

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Dynamics of Coupled Structures, Volume 1

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Abstract

The Impulse Based Substructuring (IBS) method has been proposed lately as an alternative approach to evaluate the dynamic response of a system, using the experimentally determined Impulse Response Functions (IRFs) of its components. In previous research a first experimental IBS analysis was performed using measurements on two interface points of a POM bar. It was observed that the IRFs obtained from the imperfect impulses (by means of impact hammer testing) result in stability issues in the substructuring analysis.

To obtain IRFs associated with a “true” Dirac impulse, several approaches are discussed. It is known that frequency domain averaging leads to small phase errors and thereby non-causality in the IRF obtained through inverse Fourier transformation. Alternatively a time-domain approach is presented which allows for averaging of multiple impacts while avoiding Fourier transformations. By writing the convolution product of the dynamic system using a Toeplitz matrix, the IRF can be found from solving a least-square linear system. To improve efficiency, the system can be formulated as an inverse filter operation. The time-domain procedure is illustrated by application to the one-dimensional POM bar.

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Notes

  1. 1.

    For now, displacements IRFs are considered in the derivation.

  2. 2.

    Note that if Q = N, F would be a lower triangular square matrix and the solution looses its least-square property. In that case, it follows from forward substitution that the first element y 1 is fully determined by f 1, which is normally very small. This results in a highly unstable determination of y. This problem was already reported in [9].

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Author information

Authors and Affiliations

  1. Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Section Engineering Dynamics, Delft University of Technology, Mekelweg 2, 2628CD, Delft, The Netherlands

    M. V. van der Seijs, P. L. C. van der Valk & T. van der Horst

  2. Faculty of Mechanical Engineering, Institute of Applied Mechanics, Technische Universität München, Boltzmannstr. 15, 85748, Garching, Germany

    D. J. Rixen

Authors
  1. M. V. van der Seijs
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  2. P. L. C. van der Valk
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  3. T. van der Horst
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  4. D. J. Rixen
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Corresponding author

Correspondence to P. L. C. van der Valk .

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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van der Seijs, M.V., van der Valk, P.L.C., van der Horst, T., Rixen, D.J. (2014). Towards Dynamic Substructuring Using Measured Impulse Response Functions. 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_6

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  • DOI: https://doi.org/10.1007/978-3-319-04501-6_6

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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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