Investigation on the reflection and transmission of Lamb waves across a rectangular notch

This paper is to derive the reflection and transmission coefficients of Lamb waves incident on a rectangular notch in an elastic plate by means of small local matrices instead of the single big global matrix as in traditional analyses. Several local wave form matrices are composed to represent the characteristics of each scattering process, and the reflection and transmission coefficients across the notch of a multimode Lamb wave are calculated 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 notch boundary. Efficacy of the method is illustrated by determining the transmission and reflection coefficients of S_so and A_o mode waves incident on a rectangular notch in an aluminum plate as functions of notch dimensions.