10 April 2008 The analytical trispectrum for multiple degree-of-freedom systems possessing cubic nonlinearity
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Higher-order spectra have become a useful tool in spectral analysis, particularly for identifying the presence and sometimes type of nonlinearity in a system. Two such spectra that have figured prominently in signal processing are the bispectrum and trispectrum. The bispectrum is well-suited to capturing the presence of quadratic nonlinearities in system response data while the trispectrum has proved useful in detecting cubic nonlinearities. In a previous work, the authors developed an analytical solution for the auto-bispectrum for multi-degree-of-freedom systems. Here this analysis is extended to the trispectrum. Specifically, an expression is developed for the trispectral density of a multi-degree-of-freedom system subject to Gaussian excitation applied at an arbitrary location. The analytical expression is compared to those obtained via estimation using the direct method.
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Jonathan M. Nichols, Jonathan M. Nichols, Attilio Milanese, Attilio Milanese, Pier Marzocca, Pier Marzocca, "The analytical trispectrum for multiple degree-of-freedom systems possessing cubic nonlinearity", Proc. SPIE 6935, Health Monitoring of Structural and Biological Systems 2008, 69350O (10 April 2008); doi: 10.1117/12.776495; https://doi.org/10.1117/12.776495

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