Simple formulas for transmission and reflection coefficients of a Lamb wave by multiple defects

With conventional methods such as the finite element analysis and the mode matching technique, the Lamb wave scattering analysis for multiple defects inevitably needed a very large global matrix that was frequently over affordable calculation resource capacity. In this paper, a new efficient methodology to analyze the scattering of Lamb waves by multiple notches is investigated for rapid inspection of defects in a plate. The scattering phenomenon induced by multiple notches is recursively reorganized as a dual defect problem which is interpreted as being composed of four individual processes. The scattering effects induced by each notch were summarized in so called scattering graphs. Then, the eventual scattering of the Lamb waves by the notch was expressed as simple linear equations determined by the scattering graphs. Based on the analysis, the formulas representing the reflection and transmission coefficients of Lamb waves at rectangular multiple defects in a plate are derived in the steady-state domain. The new formulas enable very rapid and easy evaluation of the amplitudes and phases of the scattered waves for an infinite number of scattering cycles.