Prediction and measurement of nonpropagating Lamb modes at the free end of a plate when the fundamental antisymmetric mode A0 is incident.

Reflection of Lamb waves when the fundamental mode A0 is incident at the free end of a plate is studied, in order to identify the extent to which the generation of nonpropagating modes influences the field local to the end of the plate. Semi-analytical predictions, finite element simulations, and experimental measurements are presented for frequencies below the A2 cutoff. First it is shown, for frequencies below the A1 cutoff, that reflection of the A0 mode is accompanied by a delay in phase, and that there is significant additional motion due to nonpropagating modes within about five plate thicknesses of the end. The extend of this additional motion in the vicinity of the end of the plate is demonstrated by subtracting the contribution of the propagating modes from the displacement field. The wave field at frequencies above the A1 cutoff is more complex because the A1 as well as the A0 propagating modes are present at the end of the plate. Nevertheless, it has still been possible, using semi-analytical predictions and finite element simulations, to demonstrate the additional motion due to the nonpropagating modes.

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

An analysis of the reflection of the fundamental Lamb mode s0 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 s0 mode.

The low-frequency reflection and scattering of the S0 Lamb mode from a circular through-thickness hole in a plate: Finite Element, analytical and experimental studies.

A study of the interaction of the S0 Lamb wave with a circular through-thickness hole in a plate is presented. The study is limited to the nondispersive frequency range of this wave, in which the distributions of stress and displacement are simple. This allows a Finite Element analysis to be undertaken using a two-dimensional membrane discretization. Predictions of the direct reflection of the S0 mode and the lateral scattering of the SH0 mode are made for a range of diameters of the hole. At the same time, an analytical solution based on modal superposition is developed, and this is also used to predict the reflection and scattering coefficients. Both sets of predictions are validated by experimental measurements. It is found that the trends of the reflection coefficients for different hole diameters, frequencies and distances from the hole satisfy a simple normalization. On a detailed scale, the functions exhibit undulations which are shown to result from the interference of the direct reflection with secondary reflections which arrive slightly later.

The low frequency reflection characteristics of the fundamental antisymmetric Lamb wave a0 from a rectangular notch in a plate.

An analysis of the reflection of the fundamental Lamb mode a0 from surface-breaking rectangular notches in isotropic plates is presented. The results are obtained from finite element time domain simulations together with experimental measurements. 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. The reflection coefficient, when plotted as a function of the notch width, exhibits a cosinusoidal periodic shape, and this is explained by interference between the separate reflections from the start and the end of the notch. The reflection coefficient, when plotted as a function of notch depth, shows that in general the reflection increases with both frequency and notch depth, but the shapes of the functions are complex and there are some surprising features. An analysis of the reflection from cracks using the S-parameter scattering approach and some simplified descriptions of the crack-opening behavior yields physical explanations of the nature of these reflection functions. It is found that opening of the crack can be described adequately by a quasistatic assumption only when the crack is small, and in other cases a ray theory approach is more representative. The reflection function is shown to be a result of contributions from both the axial stress and the shear stress in the wave, and the relative importance of these varies with the crack depth and the frequency.