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

摘要

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 S_0 Lamb mode occur. The secondary SH_0 plate wave mode generated by mode conversion from the 45° incident S_0 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 Lame mode (where there is no in-plane surface displacement), the in-plane through-thickness displacement profile of the incident S_0 Lamb mode becomes incompatible with that of the SH_0 plate mode, and the mode conversion phenomenon is thus severely compromised.