The analytical trispectrum for multiple degree-of-freedom systems possessing cubic nonlinearity

Jonathan M. Nichols; Attilio Milanese; Pier Marzocca

doi:10.1117/12.776495

10 April 2008 The analytical trispectrum for multiple degree-of-freedom systems possessing cubic nonlinearity

Jonathan M. Nichols, Attilio Milanese, Pier Marzocca

Proceedings Volume 6935, Health Monitoring of Structural and Biological Systems 2008; 69350O (2008) https://doi.org/10.1117/12.776495
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2008, San Diego, California, United States

Abstract

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.

Citation Download Citation

Jonathan M. Nichols, Attilio Milanese, and 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); https://doi.org/10.1117/12.776495

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