## 1 Introduction  
Cylindrical structures are widely used and play an extremely important role in industrial fields, for example in rocket shells, turbine shafts, engine crankshafts, train axles, pipelines, wind turbine towers, pressure vessels, etc. Cylindrical structures usually work under very tough conditions that involve bearing cyclic loads, impact loads, corrosion, high or low temperatures, and so on, and are prone to crack initiation [1; 2; 3]. Crack initiation and growth threaten the safety of structures, and would result in serious consequences such as casualties and significant financial losses. In practice, cracks initiate predominantly at the surface [4]. Therefore, it is of utmost importance that surface cracks on cylindrical structures are detected. A variety of methods have been developed for the efficient detection of cracks on cylinders, such as optical fibers [5], electrical resistance [6], vibration detection [7], magnetic induction [8], infrared thermography [9], and ultrasound testing [10; 11; 12; 13]. Among them, the ultrasound testing technique has been widely used due to its relatively high spatial resolution, portable operation, high performance ratio, and high effectiveness in damage detection. However, the application of traditional ultrasonic techniques is limited, especially in environments of high temperature and radiation. In addition, traditional ultrasonic techniques are difficult to apply to the curved surface for the coupling difficulty of traditional transducers [14]. Non-contact ultrasonic techniques are of practical importance, since it permits making ultrasonic measurements at elevated temperatures, in corrosive and other hostile environments, in geometrically difficult-to-reach locations, at a remote distance from the test structure [15]. Currently, non-contact ultrasonic techniques are practicable using air-coupled transducers [16; 17], optical interferometers [18; 19], electromagnetic acoustic transducers (EMATs) [20; 21], and laser generation. Since the 1960s, pulsed lasers have emerged as an alternative method for the generation and detection of ultrasound. Laser ultrasonic techniques provide a number of advantages over traditional ultrasonic methods such as high spatial resolution, non-contact generation, and distant testing. Laser ultrasonic techniques are very suitable for the detection of the surface crack on the curved surface [22; 23; 24; 25; 26; 27; 28]. In previous works, the propagation of ultrasound generated by a pulsed laser on the cylinder was studied both theoretically and experimentally. [PERSON] [22] found that there was a strong phase shift as the wave propagated along the circumferential path of cylindrical specimens, and the phase shift was directly related to the radius of the curvature and, to an extent, was much more sensitive than dispersion. [PERSON] [23; 24] presented 3D and 2D models that predict the acoustic waves generated by a laser point pulse and line pulse in a transversely isotropic cylinder. [PERSON] et al. [25] developed a numerical approach to efficiently study the phase shift effects on different materials, curvatures, and frequencies. [PERSON] and [PERSON] [26] applied laser ultrasonic techniques for the detection of surface-breaking slots in steel cylinders, and the results indicated that defects of lower size had a cumulative effect on the reflected Rayleigh waves. [PERSON] et al. [27; 28] established a finite element model (FEM) to investigate the laser-induced circumferential waves of a hollow cylinder with a crack, and the results showed that the existence of surface cracks and inner cracks generated a bipolar waveform between the S\({}_{0}\) mode and A\({}_{0}\) mode in the circumferential waves. To the author's knowledge, although there have been many studies on the propagation of ultrasound generated by a pulsed laser on the solid cylinder, little research has been devoted to detecting the surface crack on the cylindrical structures, using laser ultrasonics [26; 27; 28].