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

With conventional methods such as the finite element analysis and the modematching technique, the Lamb wave scattering analysis for multiple defectsinevitably needed a very large global matrix that was frequently over affordablecalculation resource capacity. In this paper, a new efficient methodology toanalyze the scattering of Lamb waves by multiple notches is investigated forrapid inspection of defects in a plate. The scattering phenomenon induced bymultiple notches is recursively reorganized as a dual defect problem which isinterpreted as being composed of four individual processes. The scatteringeffects induced by each notch were summarized in so-called scattering graphs.Then, the eventual scattering of the Lamb waves by the notch was expressed assimple linear equations determined by the scattering graphs. Based on theanalysis, the formulas representing the reflection and transmission coefficientsof Lamb waves at rectangular multiple defects in a plate are derived in thesteady-state domain. The new formulas enable very rapid and easy evaluation ofthe amplitudes and phases of the scattered waves for an infinite number ofscattering cycles.