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Proceedings Paper

Development of higher-order spectra for randomly excited quadratic nonlinear systems: Volterra functional series approach
Author(s): P. Marzocca; J. M. Nichols; M. Seaver; S. T. Trickey; A. Milanese
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Paper Abstract

Higher order spectral analysis techniques are often used to identify nonlinear interactions in modes of dynamical systems. More specifically, the auto and cross- bispectra have proven to be useful tools in testing for the presence of quadratic nonlinearities based on a system's stationary response. In this paper a class of mechanical system represented by a second-order nonlinear equation of motion subject to random forcing is considered. Analytical expressions for the second-order auto- and cross-spectra are determined using a Volterra functional approach and the presence and extent of nonlinear interactions between frequency components are identified. Numerical simulations accompany the analytical solutions to show how modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. A closed-form solution of the Bispectrum can be used to help identify the source of non-linearity due to interactions at specific frequencies. Possible applications include structural health monitoring where damage is often modeled as a nonlinearity. Advantages of using higher-order spectra techniques will be revealed and pertinent conclusions will be outlined.

Paper Details

Date Published: 11 April 2007
PDF: 10 pages
Proc. SPIE 6532, Health Monitoring of Structural and Biological Systems 2007, 65320W (11 April 2007); doi: 10.1117/12.715328
Show Author Affiliations
P. Marzocca, Clarkson Univ. (United States)
J. M. Nichols, Naval Research Lab. (United States)
M. Seaver, Naval Research Lab. (United States)
S. T. Trickey, Naval Research Lab. (United States)
A. Milanese, Clarkson Univ. (United States)


Published in SPIE Proceedings Vol. 6532:
Health Monitoring of Structural and Biological Systems 2007
Tribikram Kundu, Editor(s)

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