A Nonlinear Approach to the Delamination Characterization of Solid Structures Using Impact Response—Part II: Volterra-Series Formulation and Bispectral Analysis
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Sardahi, Yousef
Salem, Asad
Huang, Loulin
Wait, Isaac
Chen, Gang S
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MDPI AG
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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.
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4017 Mechanical engineering, 4901 Applied mathematics, nonlinear vibration, delamination detection, impact response, impact echo, Volterra series, bispectrum, higher-order spectrum, structural health monitoring, concrete structures
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Vibration, ISSN: 2571-631X (Online), MDPI AG, 9(3), 57-57. doi: 10.3390/vibration9030057
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© 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
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Except where otherwise noted, this item's license is described as Creative Commons Attribution CC BY 4.0