A mathematical model of the Lamb wave reflection at a two-dimensional rectangular notch

Abstract

Due to the long-range propagation ability of the Lamb wave, defect locations can be effectively detected. However, the evaluations of the defects are not yet quantitative because of the unsolved complex relation between the defect morphology and the signal detected. In this paper, to reveal the reflection phenomena of the Lamb wave, a simple mathematical model was proposed and evaluated. In the reflection of the Lamb wave at a defect in a plate, mode conversions among the specific propagation modes of the Lamb wave occur. The mathematical model proposed here took the mode conversion phenomena into consideration. It was confirmed that the mathematical model agreed very well with the experimental results. In order to improve the mathematical model, an interesting assumption of the regrowth process from scattered bulk waves to the Lamb wave initiated just after a discontinuity was also discussed as a modified model.