A Nonlinear Approach to the Delamination Characterization of Solid Structures Using Impact Response—Part II: Volterra-Series Formulation and Bispectral Analysis

Abstract

This study develops a third-order Volterra-series and bispectral framework for examining nonlinear vibration behavior at a delaminated region under impact excitation. The local response is represented by a nonlinear oscillator with quadratic and cubic stiffness terms, and the corresponding Volterra formulation relates these terms to the fundamental, second-harmonic, and third-harmonic response components. Bispectral analysis is then applied to measured responses above an artificial delamination under very small and small impact conditions. Within the calibrated frequency region, the very-small-impact response exhibits a relatively concentrated bispectral distribution, whereas the small-impact response exhibits a broader and more distributed pattern. The third-order cumulant shows a corresponding change from a localized to a more distributed lag-domain structure. Because the records are independently normalized, absolute bispectrum magnitudes are not compared quantitatively. An equal-duration sensitivity analysis using 614 samples for both conditions confirmed that the broader small-impact bispectral distribution persists after controlling for record duration. The results demonstrate how bispectral measures complement conventional spectral analysis by describing changes in third-order statistical structure and phase relationships among frequency components. The findings are interpreted as a proof-of-concept comparison at a known delamination location rather than as a generalized delamination-identification criterion.