Modeling and detection of delamination in a composite beam: A polyspectral approach

This work considers the difficult problem of detecting delamination in a composite beam structure based on a polyspectral analysis of the structure's vibrational response. First, a low-dimensional model of the structure is presented that captures the delamination-induced nonlinearity and shows how it influences the beam's dynamic response. A Volterra series solution is then used to approximate the nonlinear beam response. The associated Volterra kernels are derived and then substituted into previously obtained expressions for the power spectral, auto-bispectral and auto-trispectral density functions for multi-degree-of-freedom systems subject to Gaussian distributed, random inputs. The influence of the delamination on the polyspectra is then explored with respect to both delamination size and depth. Specifically, it is shown how the dominant peaks of the polyspectra relate directly to these delamination parameters. The limits of polyspectral approaches to delamination detection are presented.