The reflection and transmission of Lamb waves across a rectangular crack as a function of the crack geometry

This paper is to derive the reflection and transmission coefficients of Lamb waves incident on a rectangular crack in an elastic plate by means of small local matrices. The repeated and sequential scattering phenomenon at the crack is analyzed by introducing three independent processes according to the boundary shape of the crack and the direction of the wave propagation. Several local wave form matrices are composed to represent the scattering characteristics of each process, and the reflection and transmission coefficients of a multimode Lamb wave are calculated across the crack per each scattering cycle. By the superposition rule, the transmitted and reflected waves from all the cycles are summed to determine the overall steady state responses at the crack boundary. Efficacy of the method is illustrated by determining the transmission and reflection coefficients of S₀ and A₀ mode waves incident on a crack in an aluminum plate as functions of crack dimensions.