Development of higher-order spectra for randomly excited quadratic nonlinear systems: Volterra functional series approach

P. Marzocca; J. M. Nichols; M. Seaver; S. T. Trickey; A. Milanese

doi:10.1117/12.715328

11 April 2007 Development of higher-order spectra for randomly excited quadratic nonlinear systems: Volterra functional series approach

P. Marzocca, J. M. Nichols, M. Seaver, S. T. Trickey, A. Milanese

Author Affiliations +

Proceedings Volume 6532, Health Monitoring of Structural and Biological Systems 2007; 65320W (2007) https://doi.org/10.1117/12.715328
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2007, San Diego, California, United States

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.

Citation Download Citation

P. Marzocca, J. M. Nichols, M. Seaver, S. T. Trickey, and A. Milanese "Development of higher-order spectra for randomly excited quadratic nonlinear systems: Volterra functional series approach", Proc. SPIE 6532, Health Monitoring of Structural and Biological Systems 2007, 65320W (11 April 2007); https://doi.org/10.1117/12.715328

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