applied sciences Article  
An Efficient Damage Quantification Method for Cylindrical Structures Enhanced by a Dry-Point-Contact Torsional-Wave Transducer  
[PERSON] (c)  
Yongdong Pan  
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China; [EMAIL_ADDRESS]. As an advanced level to damage detection and localization, quantification of damage sizes is conducive to the evaluation of structural remaining life, thus being highly required in engineering applications. Relevant to this, extensive studies have been conducted to investigate the influence of damage size on the guided wave reflection and transmission in cylindrical structures [21; 22; 23; 24; 25; 26; 27]. For example, [PERSON] developed a general theoretical framework to analyze the characteristics of guided wave scattering induced by circumferential cracks in hollow cylinders with S-parameter formalism [23]. [PERSON] et al. presented a systematic numerical investigation on the reflection of T(0,1) and L(0,2) mode waves from different sizes of damage in terms of their axial width, depth, and circumferential extent [24]. [PERSON] and [PERSON] analyzed the influence of the crack depth on the mode conversion behaviors in a pipe from both numerical and experimental perspectives [25]. Despite these investigations on wave-damage interaction in cylindrical structures, research on damage quantification as an inverse problem is less reported [28; 29; 30]. Among a few existing studies, [PERSON] and [PERSON] proposed a synthetic focusing imaging method and demonstrated the strong correlation between the indices extracted from the damage image and defect size with the aid of finite element simulations [28]. However, they didn't directly quantify the size of defects due to the lack of a comprehensive database of the wave-damage interaction. [PERSON] et al. proposed a signal-processing-based method to quantify the defect size in a gas pipe [29]. The Hilbert-Huang transform was used to decompose the reflection signals from the two edges of the defect so that the defect width was successfully determined. However, the method becomes less accurate when the damage width decreases. Moreover, the depth of the defect cannot be determined. To the best of our knowledge, methods for damage quantification in cylindrical structures are still largely insufficient and under development. In practical applications, proper transducers and their installations are vital to ensure the successful generation and reception of the desired guided waves. Three types of transducers are widely used in the literature for cylindrical structures: magnetostrictive, electromagnetic-acoustic, and piezoelectric transducers. For example, [PERSON] et al. permanently bonded the magnetostrictive transducers on a pipe for the excitation and reception of the T(0,1) mode wave [31]. [PERSON] et al. used the piezoelectric discs and the corresponding wave coupling blocks to excite and receive guided waves in a steel rod for damage detection [16]. [PERSON] and [PERSON] developed a complex electromagnetic-acoustic transducer system for a pipe and tested its long-term stability [32]. [PERSON] et al. comprehensively reviewed the common transducer types for pipe inspections [20]. In most existing cases, a miscellaneous installation of the transducers is required such as bonding or mechanical installation with accessories, which may deteriorate the efficiency of damage identification. In this work, we propose a damage quantification method using a non-dispersive torsional wave in the low-frequency range for cylindrical structures under the roof of the pulse-echo scheme. Using a dry-point-contact (DPC) torsional-wave transducer, damage quantification can be efficiently achieved without special considerations on its installation. The rest of the paper is arranged as follows. Theoretical analyses are first carried out to investigate the influence of the defect size on the torsional wave reflections in Section 2.