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Development of Higher-Order Spectras for Randomly Excited Non Linear Multi-Degrees-of-Freedom Systems
Higher order spectral analysis techniques are often used to identify nonlinear interactions in modes of complex dynamical systems. The bispectrum and and tri-spectrum have proven to be useful tools in testing for the presence of quadratic and cubic nonlinearities based on a systemís stationary response. In this paper a class of M-DOF mechanical system represented by a second-order nonlinear ordinary differential equation subject to random forcing is considered. Analytical expressions for the second-and third order auto- and cross-spectras 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. Further we show how the proposed technique can be used to identify the source of non-linearity due to interactions at specific frequencies. Such identification tools can be used as a benchmark for validation of nonlinear analysis methods associated to structural health monitoring techniques and to reduce the burden associated with these methods.

PhD Student: Attilio Milanese
Investigators: Pier Marzocca
Sponsor: ASEE - ONR - NRL
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