Low-frequency reflection characteristics of the s0 Lamb wave from a rectangular notch in a plate

Abstract

An analysis of the reflection of the fundamental Lamb mode $s_0$ from surface-breaking rectangular notches in isotropic plates is presented. The results are obtained from finite element time domain simulations together with experimental measurements. Very good agreement is found between the simulations and the measurements. Results are shown for a range of notch widths and depths, including the special case of a crack, defined as a zero-width notch. An interference phenomenon is identified which explains the periodic nature of the reflection coefficient when plotted as a function of notch width. Finally, an analysis using the S-parameter approach and both low and high frequency asymptotic analyses yields physical explanations of the nature of the reflection behavior from the cracks. It is found that the low frequency (quasistatic) approximation may be used accurately for cracks up to about a quarter of the plate thickness, provided that the quasistatic crack-opening function is chosen such that bending of the plate is omitted. At higher frequencies and depths the functions tend towards the high frequency (ray theory) predictions but these are never accurate models within the nondispersive frequency range of the $s_0$ mode.