Farouk Benmeddour

Detection and localization of a defect in a reverberant plate using acoustic field correlation

Greens function can be retrieved from cross-correlation of a diffuse field generated by noise sources. Today, this important result is the fundamental of several passive imaging techniques. The aim of this paper is to establish the suitability of these methods to detect and locate a defect in a reverberant elastic plate. The relations between the noise cross-correlation function over a few number of noise sources and the imaginary part of the Greens function are derived and numerically validated. Then we show through numerical experiments that this technique is exploitable for defect detection and localization in a differential mode, despite a non-perfect estimation of the Greens functions. Finally, a filtering technique based on the singular value decomposition is shown to improve the detection.

Numerical investigation of the functionally graded materials by the interaction of the plate guided waves with discontinuities and cracks

This work intends to give a better comprehension of the guided wave interactions with damage in a functionally graded material (FGM). For this purpose, a two dimensional finite element (FE) method is used to analyse the near field surrounding the damage. Then, the expansion of the solution into sums of guided modes enables the determination of the reflection and transmission coefficients of each existent mode. The determination of the dispersion curves is ensured by the way of the so called semi-analytical finite element (SAFE) method applied to the one dimensional inlet and outlet cross-sections. Results are obtained by solving the global system of the 2D hybrid FE-SAFE method. The latter has the benefit to study an arbitrary shape-like damage in an infinite structure having the same shape by translation in the propagation direction in a fast and efficient way. The work aims to predict the propagation and interactions of plate guided waves with discontinuities in a functionally graded material composed o...

Numerical study of the cross-talk effects in acoustical transducer arrays and correction

Cross-talk in acoustical transducer arrays is an undesirable phenomenon which decreases seriously the performances of these arrays. Indeed, when one element of the array is driven, it generates parasitic displacement fields at the radiating surfaces of the neighboring elements, which changes the directivity of the antenna. To well understand this phenomenon a transducer array similar to those used in medical imaging and NDT applications was modelled by finite element method. The research work investigated systematically the effects of the cross-talk. Firstly, it inspected the acoustical and mechanical cross-talk throughout the propagating medium and the filling material. Secondly, it studied the influence of the matching layer on the acoustical performances of the transducer. It was shown that the filling material and the matching layer are the major factors contributing to this phenomenon. In order to cancel the cross-talk a correction method previously developed by the author has been used. This solutio...

Reverberation of flexural waves scattered by a local heterogeneity in a plate

A statistical model is proposed to relate the scattering properties of a local heterogeneity in a plate to the statistical properties of scattered and reverberated flexural waves. The contribution of the heterogeneity is isolated through the computation of differential signals consisting of a subtraction of the signals recorded after and before introduction of the heterogeneity. The theoretical expression of the average reverberation envelope of these differential signals is obtained as a function of the scattering cross-section of the heterogeneity. Successful numerical and experimental validations in various cases of canonical heterogeneities with known scattering cross-sections are shown. These satisfying results offer a way to estimate the scattering cross-section of an unknown scatterer from the reverberated differential signals.

Prediction of average propagation characteristics in polygonal reverberant plates for experimental feature extraction

While exploitation of reverberant signals inside bounded media of low acoustic attenuation is customary in room acoustics, it is not so common in NDT&E. Yet, such diffuse signals potentially contain useful quantitative information about the medium and source(s) properties and are very sensitive to either localised or distributed structural changes. Provided proper data extraction techniques are available, it could therefore be advantageously exploited for structural characterisation using only a small set of sensors. Specifically, in this work, we aim at retrieving either information about the source position, or about the mechanical properties of a plate-shaped structure. A statistical time-domain description of the reverberant propagation in plates is developed using the image source method. The average density of received wavepackets due to multiple reflections at the medium boundaries is deduced from the spatial distribution of the image sources. Then, the mathematical expectation (or ensemble average) of the signal envelope or correlation function is theoretically derived, taking into account the dispersive nature of the plate wave (Lamb waves). The relationships between the reverberation properties and structural parameters such as the group velocity and the plate surface are thus explicitly expressed. A major point is that the reverberant behaviour is shown to be governed by a limited set of parameters, thus leading to a significant reduction of the problem complexity. First, by comparison with both numerical and experimental results, the model is shown to correctly predict the average reverberation behaviour of polygonal plates of various shapes and sizes. Then, by fitting the late envelopes of experimental signals to the theoretical expressions provided by the model, a number of terms involving the values of structural parameters can be estimated. Finally, by considering additional relations obtained from the early characteristics (treated in a deterministic manner) of the reverberation signals, it is shown possible to extract useful structural parameters. Possible practical applications in terms of structural characterisation and/or source localisation without any time measurement nor trigger synchronisation between the source and the receiver, and without the knowledge of the emitted signal are illustrated. These results show promising potential in the scope of blind parameter estimation or passive source or defect detection.

Characterization of a local scatterer in a plate from reverberation of flexural waves

In media where acoustic waves are subject to multiple propagation paths (scattering or reverberation), recorded acoustic signals present a random aspect. Still, such signals carry some information about the medium, and ensemble averaging can give access to the estimation of a number of useful parameters. A well-known example, in room acoustics, is the estimation of absorption coefficients of walls from average decrease of the reverberation envelopes. In the work reported here, we have proposed a statistical model allowing to relate the scattering properties of a local heterogeneity (defect) to the average properties of reverberated acoustic signals in a solid plate. A theoretical expression of the averaged envelope of signals produced by scattered and reverberated flexural waves has been derived and both numerically and experimentally validated. A simple curve-fitting procedure applied to signals recorded on a few receivers then allows an experimental estimation of the scattering cross-section of the hete...

Generation of a Selected Lamb Mode by Piezoceramic Transducers: Application to Nondestructive Testing of Aeronautical Structures

The motivation of the this work is highlighted by the need for the Non-Destructive Testing (NDT) of aircraft, petrochemical and naval structures. Functioning conditions of these structures and the time factor can lead to serious damage. The most appropriate NDT technique to plate-like structures seems to be guided ultrasonics Lamb waves [1]. These waves can carry out energy over long distances and have the potential to be sensitive to several types of defects. Consequently, their use allows fast and efficient inspections of industrial structures. However, the multimode and dispersive nature of Lamb modes make the interpretation of the received ultrasonic signals complex and ambiguous in presence of discontinuities. Moreover, the generation and reception of a selected Lamb mode by transducers remains a difficult task due to the complexity of guided waves.

Application of Piezoelectric Transducers in Structural Health Monitoring Techniques

The technological advances of recent years have contributed greatly to the prosperity of the society. An important element of this prosperity is based on networks of inland, sea, and air transports. However, security in all transport networks remains a major challenge. More specifically, many researches in the field of aeronautics were done to increase the reliability of aircrafts. The themes of NDT (Non Destructive Testing), and more precisely the concept of SHM (Structural Health Monitoring), have thus emerged.

Construction of symmetrical and asymmetrical notches from elementary steps in isotropic plates

The interactions of the fundamental Lamb modes with discontinuities in an isotropic structure will be presented and analyzed in a simple and a fast way. The key point is to decompose the symmetrical or asymmetrical notch into two elementary steps. The fundamental antisymmetrical and symmetrical Lamb modes contributions are separated by means of the simple arithmetic operations of addition and subtraction. The power reflection and transmission coefficients are then computed with the well‐known average power flow equation described in a previous work [NDT&E international, Vol. 41, p.1‐9 (2008)]. Using these coefficients, the symmetrical notch can be constructed from one elementary symmetrical step while the asymmetrical notch is constructed from the superposition of asymmetrical down‐ and up‐steps. Mode conversions phenomena are observed and analyzed for the asymmetrical steps and notches case. Finally, an experimental device is realized to test aluminum plates with different notch depths. Good agreement is found between experimental and numerical results.