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An analytical formulation of bispectral densities for multiple degree-of-freedom systems

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Abstract

Expressions for the bispectral density functions for multi-degree-of-freedom spring–mass–damper systems possessing quadratic nonlinearities and subject to Gaussian excitation are derived. The derivation uses a Volterra-series model for the system response and yields expressions for both auto-spectra, where the output of only one degree-of-freedom is used, and cross-spectra, where the bispectral density contains multiple output-response time series. The proposed formulation is used to identify the presence and location of quadratic nonlinearities in multiple degree-of-freedom systems. Results show that the ability to detect and localize nonlinearity is heavily dependent on which particular bispectral density is utilized.

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Authors and Affiliations

  1. Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, 13699-5725, USA

    P. Marzocca & A. Milanese

  2. Naval Research Laboratory, 4555 Overlook Ave., Washington, DC, 20375, USA

    J. M. Nichols

Authors
  1. P. Marzocca
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  2. J. M. Nichols
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  3. A. Milanese
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Correspondence to P. Marzocca.

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Marzocca, P., Nichols, J.M. & Milanese, A. An analytical formulation of bispectral densities for multiple degree-of-freedom systems. J Eng Math 67, 351–367 (2010). https://doi.org/10.1007/s10665-009-9349-0

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  • DOI: https://doi.org/10.1007/s10665-009-9349-0

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