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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 system’s
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. |
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PhD Student: Attilio Milanese |
Investigators: Pier Marzocca |
Sponsor: ASEE - ONR - NRL |
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