The effect of frequency on secondary wave mode generation for ultrasonic health monitoring of fatigue damaged plate structures

Abstract

A computational frequency analysis of secondary wave mode generation is considered in this paper. Secondary wave mode conversion at the tip of a through‐thickness slit in a circular isotropic plate is analysed similar to a classical Sommerfeld's diffraction problem. The analysis is useful for quantitative non‐destructive evaluation of fatigue cracked plate structures that involve propagation of a single wave mode (a vertically polarised symmetric Lamb mode) and measurement of the amplitude of a new mode (a horizontally polarised shear mode). A two‐dimensional finite element model is first introduced as a baseline reference for the non‐dispersive scenario. This model is used to study the effect that P‐wave angle of incidence has on the mode converted S‐wave from the tip of the slit. A dispersive three‐dimensional finite element model of the circular plate is then introduced at a number of frequency‐thickness products within the range 0.5–3 MHz.mm−1. Within this frequency–thickness range, significant changes to the through‐thickness displacement profiles of the incident S0 Lamb mode occur. The secondary SH0 plate wave mode generated by mode conversion from the 45o incident S0 Lamb mode at the tip of a slit is analysed to establish the efficiency of the mode conversion. Visualisations of the wave fields demonstrate that at frequency–thickness products higher than the first symmetric Lamé mode (where there is no in‐plane surface displacement), the in‐plane through‐thickness displacement profile of the incident S0 Lamb mode becomes incompatible with that of the SH0 plate mode, and the mode conversion phenomenon is thus severely compromised.