Nonlinear interface forces in “breathing” debondings of laminated beams: From formation mechanism to debonding localization

Abstract

Laminated beams have been extensively used in engineering structures due to their enhanced strength and stiffness. However, debondings can occur during manufacturing or service processes, which is a typical form of barely visible damage. Therefore, accurately localizing debondings of laminated beams is crucial for maintaining structural integrity. Within the scope of linear vibration, the existing linear interface forces (LIFs), which are distributed along interfaces between two layers of a laminated beam, feature the capability of locating an open debonding, but are not applicable to a “breathing” debonding with contact behaviour. To address this limitation, this study extends the LIFs to the realm of nonlinear vibration, by which the nonlinear interface forces (NIFs) are formulated based on the equation of nonlinear transverse motion of a beam layer. Opposite to the LIFs, which appear at the intact locations only and vanish within the open debonding region, the NIFs introduced in this study appear exclusively within the “breathing” debonding region, acting as multi-tone harmonic excitation sources to produce higher harmonics. Thereby, the mechanism of generating nonlinear harmonics by NIFs can be analytically expounded. Additionally, this study highlights the use of NIFs for the localization of debondings in laminated beams due to their inherent merit of localization. Particularly, the NIFs are reconstructed from nonlinear operating deflection shapes of a laminated beam in the absence of its material and structural parameters. The capability of the NIF approach for localizing “breathing” debondings in laminated beams is numerically verified using the finite element method and experimentally validated using a scanning laser Doppler vibrometer. The results reveal that the approach is capable of characterizing the occurrence, locations, and sizes of the debondings.