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

Abstract

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.

Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates

“…Control is important, since it has been demonstrated that meshing is an issue in studying wave scattering problems, especially for weak scatterers [19], as large variations in element sizes can cause wave scattering and beam steering. The FE models of the intact and damaged panel had identical mesh to ensure all scattered waves were induced by the defect only.…”

“…Diligent et al [19] investigated the interaction of the low-frequency S 0 Lamb wave with a circular through hole using FE, analytical and experimental approaches. Diligent et al's [19] analytical model was based on Kirchhoff plate theory and the mode superposition method.…”

Video Ultrasonics by Pulsed TV Holography: A New Capability for Non-Destructive Testing of Shell Structures

“…In Cheng and Resch (1995), an acoustic scattering model for a distribution of cracks based on generalized reciprocity theory and Kino's scattering formalism is developed and, subsequently, the numerical evaluation of the reflection coefficient of Rayleigh waves is performed. In Diligent et al (2002), an analytical model based on mode superposition for scattering problems in plates, and its application for predicting the reflection coefficient of Lamb waves from a through-thickness hole, is presented combined with FEM simulation of the scattering and also with experimental data. Other works based on modal decomposition relate the reflected and transmitted waves to the properties of specific types of flaws (Shkerdin and Glorieux 2004;Castaings et al 2002).…”

On the development and testing of a guided ultrasonic wave array for structural integrity monitoring

“…In particular, the S 0 mode has been used for tomography applications [7], as at low frequency-thickness it has the highest group velocity, i.e., the fastest arrival time. The scattering at typical structural features and defects has been studied for a variety of applications [8], [9]. Recently, the development of a localized array based on the excitation and reception of the S 0 mode using electromagnetic acoustical transducers (EMATs) acting as point sources/receivers has been reported [10].…”