Zero-group velocity combined-harmonic generation through counter-directional mixing and application for internal damage localization in composites

This paper investigates the generation of zero-group velocity (ZGV) combined-harmonic modes through the interaction of counter-directional mixing of guided waves in carbon fiber reinforced polymer (CFRP) laminated plates. The internal resonance conditions for generating ZGV combined harmonics in transversely isotropic materials are derived in detail through theoretical analysis. The ZGV mode in a [90/45/−45/0]s layered CFRP plate is calculated using the semi-analytical finite element method. Based on this analysis, a primary mode pair is selected for generating the ZGV combined-harmonic mode. The generation of the ZGV combined-harmonic mode is successfully validated via a three-dimensional finite element model simulation, which also reveals the local resonance effect of the generated S1-ZGV combined harmonic. Subsequently, the feasibility of multi-internal damage localization is validated by the use of the generated ZGV combined-harmonic mode. A B-scan approach is implemented by locally generating the ZGV combined-harmonic mode through adjusting the excitation time delay of the primary waves. The results demonstrate that the S1-ZGV combined harmonic exhibits greater sensitivity and effectiveness for accurate localization of internal damage in composites.