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Instantaneous Frequency and Damping from Transient Ring-Down Data

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Dynamics of Coupled Structures, Volume 4

Abstract

Broadband impact excitation in structural dynamics is a common technique used to detect and characterize nonlinearities in mechanical systems since it excites many frequencies of a structure at once. Non-stationary time signals from transient ring-down measurements require time-frequency analysis tools to observe variations in frequency and energy dissipation as the response evolves. This work uses the short-time Fourier transform to estimate the instantaneous parameters from measured or simulated data. By combining the discrete Fourier transform with an expanding or contracting window function that moves along the time axis, the resulting spectra are used to estimate the instantaneous frequencies, damping ratios and complex Fourier coefficients. This method is demonstrated on a multi-degree-of-freedom beam with a cubic spring attachment. The amplitude-frequency dependence in the damped response is compared to the undamped nonlinear normal modes. A second example shows the results from experimental ring-down measurements taken on a beam with a lap joint, revealing how the mechanical interface introduces nonlinear frequency and damping parameters.

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Acknowledgements

This work was funded by Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. The authors would also like to thank Matt Bonney, Brett Robertson and Fabian Schempp for sharing the experimental data they collected on the lap joint presented in Sect. 24.4. Finally, the authors would like to thank Scott Smith and Caroline Nielsen for their help developing the algorithm in Matlab and working on a graphical user interface.

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Authors and Affiliations

  1. Sandia National Laboratories, 5800 MS 0346, Albuquerque, NM, 87185, USA

    Robert J. Kuether & Matthew R. W. Brake

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  1. Robert J. Kuether
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  2. Matthew R. W. Brake
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Correspondence to Robert J. Kuether .

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Editors and Affiliations

  1. Engg Phys Dept 535 Engg Res Bldg, University of Wisconsin Madison, Madison, Wisconsin, USA

    Matt Allen

  2. MS 0557, Sandia National Laboratories, Albuquerque, New Mexico, USA

    Randall L. Mayes

  3. Lehrstuhl für Angewandte Mechanik, TU München, Garching, Bayern, Germany

    Daniel Rixen

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Kuether, R.J., Brake, M.R.W. (2016). Instantaneous Frequency and Damping from Transient Ring-Down Data. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29763-7_24

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  • DOI: https://doi.org/10.1007/978-3-319-29763-7_24

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