# Weakening Detection of Composite Structure Adhesive Layer Based on Nonlinear Guided Waves
## 6 Conclusions  
This paper presented the detection and evaluation of nonlinear phenomena in composite structures using nonlinear ultrasonic guided waves. The analysis used finite elements to investigate early-stage overall weakening and localized damage within the adhesive layer. Finally, relevant experiments were performed, leading to the following conclusions:  
1. Using the transfer matrix method, the dispersion equation for a three-layer composite structure was established. The phase velocity varies with changes in the elastic modulus and Poisson's ratio of the adhesive layer. Furthermore, the degree of variation differs across different modes and frequency ranges. On these grounds, the A1-S1 mode pair that met the phase-matching conditions was selected.
2. Simulations were conducted using the A1-S1 mode pair, resulting in a maximum error of 5.15% and a minimum of 4.38% in the group velocity. Additionally, the amplitude of the second-order harmonic and the nonlinear coefficient gradually accumulated and increased as the Lamb wave propagation distance increased. As the third-order elastic modulus of the adhesive layer increased, indicating an increase in the early-stage overall weakening of the adhesive layer, the second harmonic amplitude and nonlinear coefficient gradually increased with increasing propagation distance.
3. Signals from the undamaged model and the damaged model were almost identical, while the second-order harmonic amplitude of the damaged model increased compared to the undamaged model. For models with local damage at 40-60 mm, the  
Figure 19: Comparison of the changes in the nonlinear coefficient over propagation distance.  
Figure 18: Experimental frequency spectrum: (**a**) experiment 1; (**b**) experiment 2; (**c**) experiment 3.  
increase in the nonlinear coefficient was more significant, and there was a sudden change in the slope of the nonlinear coefficient at this position. Therefore, the approximate location of the damage can be determined by observing the sudden change in the slope of the nonlinear coefficient.
* The maximum and minimum errors between the experimental and theoretical group velocities were 6.96% and 3.82%, respectively. Additionally, the increase in the nonlinear coefficient with increasing propagation distance demonstrated the accumulative effect of the second harmonic in nonlinear guided waves.  
F.B.: software, methodology, investigation, and writing. W.W.: review and editing. X.W.: review and validation, supervision, and funding acquisition. X.L.: review and investigation. G.S.: investigation. G.T.: review. C.M.: review. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 52265020.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
Author [PERSON] was employed by the company Jiangxi Changxing Aviation Equipment Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.