Abstract
Expressions for the bispectral density functions for multi-degree-of-freedom spring–mass–damper systems possessing quadratic nonlinearities and subject to Gaussian excitation are derived. The derivation uses a Volterra-series model for the system response and yields expressions for both auto-spectra, where the output of only one degree-of-freedom is used, and cross-spectra, where the bispectral density contains multiple output-response time series. The proposed formulation is used to identify the presence and location of quadratic nonlinearities in multiple degree-of-freedom systems. Results show that the ability to detect and localize nonlinearity is heavily dependent on which particular bispectral density is utilized.
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