Guided wave propagation and scattering in pipes with axisymmetric defects under reciprocity considerations

Abstract

This paper presents a theoretical framework utilizing the reciprocity theorem to investigate the behavior of guided waves in pipe-like structures. The reciprocity theorem is first employed to derive closed-form solutions of guided waves generated by time-harmonics sources in seamless pipes. The application of this technique is then extended to address the scattering of longitudinal modes by a circumferential defect in pipes. The scattered field results are afterward validated by numerical simulations, demonstrating good quantitative agreement across various defect configurations. Furthermore, we introduce the dispersion curves superimposed by wave magnitude spectra, providing a clear visualization of wave propagation phenomena in pipes. These curves can also be utilized for optimal mode and excitation frequency selection in practical inspection processes. This study makes a significant contribution to the field of nondestructive evaluation by offering a simple and effective approach to analyzing the scattering of guided longitudinal waves in pipes. The results can enhance the accuracy and reliability of defect detection and characterization, leading to more efficient and cost-effective maintenance and repair processes.