## 6 Conclusions  
The signal enhancement of cylindrical surface waves on the cracked cylinder has been demonstrated by a fully coupled explicit finite element model. The physical mechanisms of signal  
Figure 14: Normalized SLLS peaks as a function of the depth of the crack at \(\alpha=85^{\circ}\) on a cylinder. Detection positions \(\theta\) are at 30\({}^{\circ}\), 60\({}^{\circ}\), 90\({}^{\circ}\), 120\({}^{\circ}\), and 150\({}^{\circ}\) as labeled. Cylinder diameter of (a) 20 mm and (b) 10 mm are studied.  
Figure 15: **(a)** Directivity pattern of the longitudinal waves excited by a laser line source in aluminum; **(b)** The geometric relationship between the crack and the laser source; \(h\) is the crack depth; \(\beta\) is the angle between the center of the laser line source and the direction of longitudinal wave propagation.  
enhancement of the SLLS method and the SLD method in the near field are explained by interference between the direct surface waves and various scattered waves. The simulation results indicate that the signal enhancement of the SLLS method is more sensitive to the surface crack on a cylinder than that of the SLD method, given the wider span and higher peak of the peak-to-peak variation.  
Due to the phase shift characteristic of the surface waves in the cylinder, the signal enhancement is affected by the position of detection, and the SLLS peaks at the unipolar position of the surface waves is significantly higher than that at the bipolar position. The unipolar position of the surface waves on an intact cylinder can be recognized as the approximate optimal position for the location of the surface crack using the SLLS method. The phase shift of the cylindrical surface waves is also affected by the diameter of the cylinder. To locate the surface crack on the solid cylinders with different diameters, the PSR at the diameter can first be obtained from the PSR curve, the phase shift curve can then be constructed to obtain the unipolar position of the surface waves. The unipolar position can be taken as the optimal position of detection to locate the surface crack in the SLLS method.  
The depth of the surface crack affects the longitudinal wave and induces its conversion into a surface wave in the SLLS method. Due to the directivity pattern of the propagation of the longitudinal wave, the SLLS peaks no longer follow the depth of the crack when the depth of the crack exceeds a certain range, which can be calculated from the amplitude directivity pattern of the longitudinal wave. Therefore, the enhancement of the SLLS peaks can effectively represent the changes in the depth of the crack only within a limited range, which is dependent on the directivity pattern of the longitudinal waves.  
This work presents a method to identify the location and the depth of the surface crack in the cylindrical structures. It provides a feasible way for the in-situ and non-contact detection of the surface crack on the cylinder. It is worth noting that realistic cracks are often relatively rough, are nonplanar, and can be partially closed. A future study with the method proposed in this paper will focus on the detection of realistic surface cracks in the cylinder.  
[PERSON] and [PERSON] ran the simulation; [PERSON] analyzed the data and wrote the manuscript; [PERSON] and [PERSON] reviewed the manuscript and provided supervision and guidance in this research; [PERSON] and [PERSON] edited the manuscript; all authors contributed to discussions and feedback of the manuscript. This research was funded by the National Natural Science Foundation of China under Grant Number 51375434. The authors declare no conflict of interest.