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SUMMARY Eikonal tomography has become a key approach to image lithospheric structures with surface waves recorded by dense regional arrays. Its main advantage is that phase velocities can be determined directly from phase measurements without resolving a tomographic inverse problem. Here, we apply a new smoothing spline eikonal tomography approach to a selection of 40 large (Mw larger than 6.5) teleseismic events recorded by the permanent seismic stations of the CEArray. We first apply a time–frequency filter to isolate the fundamental mode of Rayleigh waves and cross-correlate the cleaned and isolated surface wave records to measure precise relative traveltimes. The phase measurements are then unwrapped and corrected for cycle skipping. Finally, we derive phase-velocity maps from the gradient of the reconstructed traveltime fields, using the eikonal equation. We obtain finely resolved phase-velocity maps from 25 to 150 s period that are inverted to obtain a 3-D shear wave velocity model which is in good agreement with previous tomographic studies. The lithospheric architecture emerging from the phase-velocity maps and 3-D S-wave velocities correlates with surface geology and major tectonic provinces. In particular, the architecture of the narrow rift systems, the South China Craton, and the North China Craton (NCC) are revealed with unprecedented details. The South China Craton is characterized by very high velocities beneath the Sichuan Basin. The NCC shows more complex structures with two high-velocity anomalies beneath the Ordos Basin and the southeastern NCC and low-velocity anomalies beneath the Cenozoic rift systems.

SUMMARY The densification of both permanent and temporary seismic networks has raised new interest in surface wave eikonal tomography from which phase velocity maps can be obtained without resolving a tomographic inverse problem. However, eikonal tomography requires to reconstruct traveltime surfaces from a discrete number of measurements obtained at the station locations, which can be challenging. We present a new method to reconstruct these traveltime surfaces with smoothing splines discretized in a regular 2-D Cartesian grid. We impose Neumann boundary conditions so that the phase gradients on the edges of the grid are equal to the apparent slownesses of the average plane wave along the normal direction measured by beamforming. Using the eikonal equation, phase velocity maps are then derived from the norm of the gradient of the interpolated traveltime maps. The method is applied to Rayleigh waves recorded by the Southern California Seismic Network to derive phase velocity surfaces. Robust, stable and finely resolved phase velocity maps at 25 and 33 s period are obtained after averaging the phase velocity maps derived from the analysis of a selection of recent large (Mw ≥ 6.5) teleseismic events. The phase velocity map at 25 s mainly constrains the thickness of the Southern California crust, with results that are in excellent agreement with previous tomographic studies.

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Zero Group Velocity (ZGV) modes are peculiar guided waves that can exist in elastic plates or cylinders, and have proved to be very sensitive tools in characterizing materials or thickness variations with sub-percent accuracy at space resolutions of about the plate thickness. In this article we show theoretically and experimentally how such a mode can be generated as the sum-frequency interaction of two high amplitude primary waves, and then serve as a local probe of material non-linearity. The solutions to the phase matching condition, i.e. condition for a constructive non-linear effect, are obtained numerically in the mark of classical, quadratic non-linearity. The coupling coefficients that measure the transfer rate of energy as a function of time from primary to secondary modes are derived. Experiments are conducted on an aluminum plate using piezo-electric transducers and a laser interferometer, and explore the interaction for incident symmetric and anti-symmetric fundamental Lamb modes. In an experiment operated without voltage amplifier we demonstrate that the resonant nature of these ZGV modes can be leveraged to accumulate energy from long excitations and produce detectable effects at extraordinarily low input power even in such weakly non-linear material.

In this paper, a numerical method is proposed to investigate the propagation of elastic guided waves in the armors protecting cylindrical structures, such as cables and pipes, and evaluate the feasibility of using these waves in the context of non-destructive evaluation and structural health monitoring. Armors usually consist of a large number of helical wires in contact with polymeric sheaths surrounding the structure. The numerical method combines a semi-analytical finite element method written in twisting coordinates, which accounts for the continuous screw symmetry of the problem along the structure axis, with rotational Bloch conditions in the cross-section in order to account for the high order of the discrete circular symmetry. The proposed formulation allows the initial three-dimensional problem to be reduced to a two-dimensional unit cell involving only one wire, well suited for fast computations of contact problems and dispersion curves. The existence of wave modes along the two directions (screw axis and circumferential direction) is justified from a theoretical point of view by considering the metric tensor of a mixed twisting-polar coordinate system. Numerical results are presented for a typical armor of power cable, focusing on longitudinal waves propagating predominantly inside the wires. The internal part of the cable is approximated as a homogenized medium to preserve the continuous screw symmetry of the problem. A comparison with experimental measurements is carried out. The results show that the modal velocity of longitudinal waves behaves as in a single free wire above a limit frequency identified by the model. This is not the case of modal attenuation, always greater in the armor due to mechanical contact with the viscoelastic sheaths. Two modes of potential interest for the non-destructive evaluation of armors are identified. The influence of mechanical contacts on wave propagation in armors is finally discussed, including interwire contact.

Seismic metamaterials have been the subject of much recent interest, with notable conceptual advances and the demonstration of possible full-scale effectiveness in earthquake protection. Here, through a fine analysis of the dispersion properties and behavior of resonators introduced in a laboratory scale setup, we propose a strategy for the design of an efficient metaseismic barrier. When positioned onto an unconsolidated granular layer, rigid masses of nontrivial shape become elastic resonators by coupling with the relatively soft propagation medium. Additionally, they affect the mechanical boundary conditions and subsurface medium properties through the added weight. We demonstrate that all these ingredients can be rationally combined to improve the shielding effect and control the seismic waves.

International audience; In this paper, a two-dimensional formulation is proposed for modeling the mechanical behavior of helical beam-like structures subjected to bending loads. Helical structures include multi-wire cables, which are widely used in engineering applications. An accurate representation of their mechanical behavior typically requires large-size three-dimensional finite element models. The proposed formulation, written on the cross-section only, offers a tremendous reduction of computational cost. Based on the asymptotic expansion method, the formulation is derived within the framework of homogenization theory. The first-order approximation of the three-dimensional problem is obtained from the solution of two successive problems: a microscopic three-dimensional problem and a macroscopic one-dimensional problem. The latter corresponds to the equilibrium equations of a straight Navier-Bernoulli-Saint Venant beam, which effective elastic properties can be post-processed from the solution of the microscopic problem, rewritten in a helical curvilinear coordinate system (twisting system). Thanks to this coordinate system, we demonstrate that the microscopic problem can be reduced to the cross-section and solved by a two-dimensional finite element analysis. In the twisting system, it is shown that bending loads yet depend on the axial coordinate and require a specific treatment leading to separate variable solutions in the axial variable of complex type. Therefore, this paper advances one step further than previous papers in which the microscopic problem was reduced to a two-dimensional formulation with the drawback that only axial loads (extensional or torsional) could be considered. Numerical results are presented for cylinders, springs, and seven-wire strands. Good agreement with analytical solutions is achieved. Interestingly, the formulation allows an accurate analysis of mechanical contact effects on the homogenized properties.

Summary Face to an increasing traffic volumes, a poor adhesion between bitumen layers combined with weather conditions can lead to premature deterioration of pavement structures. Therefore, it is essential to resort a tack coat where the wearing course and the binder course connect, so that they work as a monolithic block. The purpose of this study, carried out by using gprMax software, is to identify a thin millimetric subsurface tack coat from a modelled bilayer of bitumen and to differentiate the signals according to the modifications of some parameters like thickness, permittivity and conductivity. The so generated large database of time signals with diverse geometric and dielectric characteristics will enable to classify the datas by a supervised machine learning method namely, Support Vector Machines (SVM). Among existing methods, the algorithm of Two-Class SVM (TCSVM) allows to split the datas in two distinct classes. One data set is described as the “adhered” class, and another as the “non adhered” class. The supervised machine learning is conducted with a resolution by global approach to use the raw data set, without any pre-processing. Finally, the binary classification appears then as a promising method to identify clearly and automatically the presence of a tack coat.

Monitoring the small variations of a medium is increasingly important in subsurface geophysics due to climate change. Classical seismic surface wave dispersion methods are limited to quantitative estimations of these small variations when the variation ratio is smaller than 10 per cent, especially in the case of variations in deep media. Based on these findings, we propose to study the contributions of the Rayleigh wave phase velocity derivative with respect to frequency. More precisely, in the first step of assessing its feasibility, we analyse the effects of the phase velocity derivative on the inversion of the fundamental mode in the simple case of a two-layer model. The behaviour of the phase velocity derivative is first analysed qualitatively: the dispersion curves of phase velocity, group velocity and the phase velocity derivative are calculated theoretically for several series of media with small variations. It is shown that the phase velocity derivatives are more sensitive to variations of a medium. The sensitivity curves are then calculated for the phase velocity, the group velocity and the phase velocity derivative to perform quantitative analyses. Compared to the phase and group velocities, the phase velocity derivative is sensitive to variations of the shallow layer and the deep layer shear wave velocity in the same wavelength (frequency) range. Numerical data are used and processed to obtain dispersion curves to test the feasibility of the phase velocity derivative in the inversion. The inversion results of the phase velocity derivative are compared with those of phase and group velocities and show improved estimations for small variations (variation ratio less than 5 per cent) of deep layer shear wave velocities. The study is focused on laboratory experiments using two reduced-scale resin-epoxy models. The differences of these two-layer models are in the deep layer in which the variation ratio is estimated as 16.4 ± 1.1 per cent for the phase velocity inversion and 17.1 ± 0.3 per cent for the phase velocity derivative. The latter is closer to the reference value 17 per cent, with a smaller error.

Water saturation profiles in concrete are essential to assess its durability and can be determined using non-destructive techniques, especially the electric and the capacitive methods. In this paper, we propose a new inversion scheme where both resistivity and permittivity measurements are inverted jointly to retrieve the saturation profile. The finite element method is used to model the measurements in 3D, the concrete having a saturation profile with depth, represented by a continuous model taking the form of a Weibull curve with four parameters. A non-linear least-squares optimization based on the Levenberg-Marquardt scheme is developed for the inversion of measurements. Results show that information gathered from both measurements enriches the reconstructed profile, leading to a more reliable estimation of saturation profiles. We believe that the joint inversion method herein developed could lead to the study of more complex phenomena, such as the coupled water-chloride ingress.

This paper presents a model reduction strategy for fast finite element analysis of continuously symmetric elastic waveguides. Accounting for continuous symmetry, the initial three-dimensional problem is first reduced to a two-dimensional quadratic eigenvalue problem based on a semi-analytical finite element method. This problem has to be solved repeatedly at multiple frequencies to determine the modal properties of the waveguide as functions of frequency (e.g. dispersion curves). Although two-dimensional, such a problem becomes costly when the problem size increases. In this paper, a specific reduction basis is proposed to project the matrix operators of the eigenvalue problem. This reduced basis is built from complex eigenvectors computed at the maximum frequency of analysis, enriched by cut-off eigenvectors, and then post-processed through a QR decomposition. Numerical results are presented for three critical test cases, involving high-frequency viscoelastic loss, curve veering phenomena, or leakage loss respectively. The reduction method turns out to be simple to implement, fast, and accurate for the complex spectrum, including attenuated waves. The time needed to build the reduced model, prior to its solution, remains short (roughly equal to a single frequency iteration of the full model). Once reduced, the eigenvalue problem can be solved more than 50 times faster than the full eigenvalue problem.

International audience; Dike management has become a major concern in France over the last 20 years after several flood disasters caused by dikes failures. The poor condition of more than 60% of the dikes in the country and the increase of flood occurrences/intensities due to global climate change obviously lead to a closer monitoring of the structures and their reinforcement. The most commonly used method for routine and crisis monitoring of dikes is based on visual inspections on the field. It allows the detection of surface indicators (i.e animal burrows, deformations, water seepage, etc.) resulting from internal disorders. However, this method is time-consuming for pluri-kilometric sections of dikes and not safe for the field operators during a flood. The DIDRO (DIke monitoring by DROnes) project develops a solution for high efficiency routine and crisis monitoring of dikes, using a UAV carrying multiple remote sensing sensors and aquatic equipment. Remote sensing sensors include LiDAR, thermal infrared, near-infrared and visible sensors and provide high resolution data of the surface of the dike. Such sensors, never combined on a UAV for this type of survey, allow the detection of a large number of surface indicators of internal and external dike disorders. Aquatic measurements consist 1) in flow velocity estimations using floating targets dropped in the river or in the sea by the UAV and 2) in a system for water turbidity estimation towed by the UAV. This system is particularly useful for the detection of erosion during a flood. Geophysical methods have been thought to be particularly useful to complement the UAV system and include electrical resistivity imagery, self potential and background seismic noise equipment. The UAV is then used to tow or to drop some of the equipments along the dike and to remotely collect data. This can be particularly useful during flooding, when accessing the dike may be dangerous. The switch from one payload configuration to another is made easy by a specific mounting system, adaptable to different types of UAV. This makes the DIDRO solution more easily deployable during flooding events. This presentation focuses on the description of the different payload configurations of DIDRO and on the specifications of the equipment used, and will present some results obtained during tests carried out on several dikes in France.

The first meters of the underground media, the Critical Zone, involve many human activities. It is also the site of disturbances due to climate change through variations in the level of the water table, hydric and mechanical modifications that increase erosion and the risks of damage or even collapse. Therefore, monitoring of the subsurface and its anthropogenic structures is currently a major challenge. Therefore, geophysical methods, especially seismic methods, which allow to evaluate the mechanical parameters of the environment, are interesting. Among them, the MASW technique based on Surface Seismic Waves estimates a 1D-profile of S wave velocities. The inverted data corresponds to the dispersion of the phase velocity (V ph ) or group velocity. However, the accuracy of the MASW inverse solutions does not discriminate Vs variations lower than a few percent. These limits are due to the current level of measurements uncertainty but also to the sensitivity of the data to the medium parameters. To overcome this key issue, we propose three methodological alternatives. The first proposes to invert the frequency derivative of Vph . The two others are based on the inversion of differential data. In the first one, it is the statistical distance between the main lobes of dispersion diagrams assimilated to histograms. In the second, it is an analytical formulation by linear approximation of Vph . These proposals show a contribution of the resolution for typical two-layer models of the subsurface, based on synthetic data and laboratory measurements by laser interferometry on resin and concrete models., Les premiers mètres du sous-sol, la Zone Critique, concentrent de nombreuses activités humaines. La ZC est aussi le siège de perturbations en raison du changement climatique à travers des variations du niveau des nappes, de modifications hydriques et mécaniques qui augmentent l'érosion et les risques de dommages voire d'effondrements. Aussi, la surveillance de la subsurface et de ses structures anthropiques est actuellement un enjeu majeur. De ce fait, les méthodes géophysiques, notamment sismiques permettant d'évaluer les paramètres mécaniques du milieu sont intéressantes. Parmi elles, la technique MASWbasée sur les Ondes Sismiques de Surface estime un profil 1D de vitesses d'ondes S. Ladonnée inversée correspond à la dispersion de la vitesse de phase (Vph ) ou de groupe.Cependant, la précision des solutions inverses par MASW ne discrimine pas les variations de Vs de quelques pourcents. Ces limites sont dues auniveau d'incertitude des mesures mais aussi à la sensibilité de la donnée aux paramètres du milieu.Pour lever ce verrou, nous proposons trois alternatives méthodologiques. La premièrepropose d'inverser la dérivée fréquentielle de Vph . Les deux autres reposent sur l'inversion de données différentielles. Dans la première, il s'agit de la distance statistique entre les lobes principaux des diagrammes de dispersion assimilés à des histogrammes. Dans la deuxième, il s'agit de formulation analytique parapproximation linéaire de Vph . Ces propositions sont appliquées à des modèles bicouches, tant sur des données synthétiques que sur des mesures de laboratoire sur du béton et par interférométrie laser sur des modèles en résines.

The first meters of the underground media, the Critical Zone, involve many human activities. It is also the site of disturbances due to climate change through variations in the level of the water table, hydric and mechanical modifications that increase erosion and the risks of damage or even collapse. Therefore, monitoring of the subsurface and its anthropogenic structures is currently a major challenge. Therefore, geophysical methods, especially seismic methods, which allow to evaluate the mechanical parameters of the environment, are interesting. Among them, the MASW technique based on Surface Seismic Waves estimates a 1D-profile of S wave velocities. The inverted data corresponds to the dispersion of the phase velocity (V ph ) or group velocity. However, the accuracy of the MASW inverse solutions does not discriminate Vs variations lower than a few percent. These limits are due to the current level of measurements uncertainty but also to the sensitivity of the data to the medium parameters. To overcome this key issue, we propose three methodological alternatives. The first proposes to invert the frequency derivative of Vph . The two others are based on the inversion of differential data. In the first one, it is the statistical distance between the main lobes of dispersion diagrams assimilated to histograms. In the second, it is an analytical formulation by linear approximation of Vph . These proposals show a contribution of the resolution for typical two-layer models of the subsurface, based on synthetic data and laboratory measurements by laser interferometry on resin and concrete models.; Les premiers mètres du sous-sol, la Zone Critique, concentrent de nombreuses activités humaines. La ZC est aussi le siège de perturbations en raison du changement climatique à travers des variations du niveau des nappes, de modifications hydriques et mécaniques qui augmentent l'érosion et les risques de dommages voire d'effondrements. Aussi, la surveillance de la subsurface et de ses structures anthropiques est actuellement un enjeu majeur. De ce fait, les méthodes géophysiques, notamment sismiques permettant d'évaluer les paramètres mécaniques du milieu sont intéressantes. Parmi elles, la technique MASWbasée sur les Ondes Sismiques de Surface estime un profil 1D de vitesses d'ondes S. Ladonnée inversée correspond à la dispersion de la vitesse de phase (Vph ) ou de groupe.Cependant, la précision des solutions inverses par MASW ne discrimine pas les variations de Vs de quelques pourcents. Ces limites sont dues auniveau d'incertitude des mesures mais aussi à la sensibilité de la donnée aux paramètres du milieu.Pour lever ce verrou, nous proposons trois alternatives méthodologiques. La premièrepropose d'inverser la dérivée fréquentielle de Vph . Les deux autres reposent sur l'inversion de données différentielles. Dans la première, il s'agit de la distance statistique entre les lobes principaux des diagrammes de dispersion assimilés à des histogrammes. Dans la deuxième, il s'agit de formulation analytique parapproximation linéaire de Vph . Ces propositions sont appliquées à des modèles bicouches, tant sur des données synthétiques que sur des mesures de laboratoire sur du béton et par interférométrie laser sur des modèles en résines.

Summary Due to a too sparse permanent seismic coverage during the last decades, the crustal structure of western France and the surrounding regions is poorly known. In this study, we present a 3-D seismic tomographic model of this area obtained from the analysis of 2-year continuous data recorded from 55 broad-band seismometers. An unconventional approach is used to convert Rayleigh wave dispersion diagrams obtained from ambient noise cross-correlations into posterior distributions of 1-D VS models integrated along each station pair. It allows to avoid the group velocity map construction step (which means dispersion curve extraction) while providing meaningful VS posterior uncertainties. VS models are described by a self-adapting and parsimonious parameterization using cubic Bézier splines. 1268 separately inverted 1-D VS profiles are combined together using a regionalization scheme, to build the 3-D VS model with a lateral resolution of 75 km over western France. The shallower part of the model (horizontal cross-section at 4 km depth) correlates well with the known main geological features. The crystalline Variscan basement is clearly associated with positive VS perturbations while negative heterogeneities match the Mesocenozoic sedimentary basins. At greater depths, the Bay of Biscay exhibits positive VS perturbations,which eastern and southern boundaries can be interpreted as the ocean-continent transition. The overall crustal structure below the Armorican Massif appears to be heterogenous at the subregional scale, and tends to support that both the South-Armorican Shear Zone and the Paris Basin Magnetic Anomaly are major crustal discontinuities that separate distinct domains.

The goal of this paper is to investigate the propagation of two-dimensional elastic Bloch waves in helical periodic structures, obeying two discrete screw symmetries about the same axis. First, a three-dimensional coordinate system is built from the two helical directions of periodicity of the problem and the radial coordinate originating from the symmetry axis. The existence of Bloch waves in bi-helical structures can be justified owing to the independence of the metric tensor of the coordinate system on both helical coordinates. Considering the elastodynamic equilibrium equations, Bloch theorem is expressed in appropriate bases to project the vector wavefields, namely the covariant/contravariant bases of the bi-helical coordinate system (or, alternatively, the cylindrical basis). From a geometrical point of view, the three-dimensional unit cell is delimited by non-plane boundaries, which must be carefully parametrized. The so-called wave finite element method is then applied to numerically solve the Bloch wave eigenproblem and the implementation of the numerical method in a bi-helical system is detailed. Owing to the cylindrical nature of the geometry, the two-dimensional propagation constants are not independent to each other. The relationship between both constants is established. The calculation of wave mode properties (wavenumbers, group and energy velocities) is performed along the helical propagation directions, as well as the straight axial and circumferential directions. Numerical validations of the overall approach are carried out for cylindrical uniform tubes and a chiral nanotube. Finally, the method is applied to a complex multi-wire structure, often encountered in energy cables, consisting of two layers of helical wires twisted in opposite directions.

A numerical model is proposed to compute the eigenmodes and the forced response of multilayered elastic spheres. The main idea is to describe analytically the problem along the angular coordinates with spherical harmonics and to discretize the radial direction with one-dimensional finite elements. The proper test function must be carefully chosen so that both vector and tensor spherical harmonics orthogonality relationships can be used. The proposed approach yields a general one-dimensional formulation with a fully analytical description of the angular behaviour, suitable for any interpolating technique. A linear eigenvalue problem, simple and fast to solve, is then obtained. The eigensolutions are the spheroidal and torsional modes. They are favourably compared with literature results for a homogeneous sphere. The eigensolutions are superposed to compute explicitly the forced response. The latter is used to reconstruct the propagation of surfaces waves. In particular, the collimation of a Rayleigh wave (non-diffracted surface wave propagating with a quasi-constant width) excited by a line source in a homogeneous sphere is recovered with the model. Based on the vibration eigenmodes, a modal analysis shows that such a wave is a superposition of fundamental spheroidal modes with a displacement confined at the equator of the sphere. These modes are the so-called Rayleigh modes, of sectoral type and high polar wavenumbers. When a thin viscoelastic coating is added to the sphere, the Rayleigh mode behaviour is recovered in a limited frequency range, allowing the generation of a collimating wave at the interface between the sphere and the coating.

In this paper, a multi-scale analysis of the effect of foam on chemo-mineralogical and microstructural features of the soil–cement–water system is presented. Time-dependent mineralogical and microstructural changes induced by foam were monitored at increasing curing times by means of X-ray diffraction, thermogravimetric analysis, scanning electron microscopy and mercury intrusion porosimetry. Addition of foam does not alter chemo-physical evolution of the soil–cement–water system in terms of either cement hydration or pozzolanic reactions. Large voids are present in the samples as footprints of air bubbles upon mixing, increasing the porosity of samples but not altering their matrix microstructure. Macroscopic behaviour of treated samples was investigated by direct shear tests. Chemo-physical evolution induced by adding cement is the main factor responsible for mechanical improvement shown by the treated samples. Sample porosity induced by adding foam plays a key role in the mechanical response of lightweight cemented samples, inducing a transition of stress–strain behaviour from brittle and dilative to ductile and contractile as foam content is increased.

Communication pour le congrès ISPRS du 4 au 10 Juillet 2021; International audience; In this paper, we present a methodology to fusion 3D visible and thermal infrared (TIR) information on a coastal landslide area located in Normandy, France. A reflex and TIR camera on-board an Unmanned Aerial Vehicle are utilized to generate a 3D visible and a thermal model using Photogrammetry. A Python-written algorithm is then used to associate the thermal scalar on the TIR model to the closest point on the visible point cloud, before applying α-blending to ease the visualization of both data sets. This methodology leads to the generation of an integrated 3D thermo-visible model, allowing the direct analysis of the surface temperatures, visible data and geometric configuration of the landslide.

The fields of applications involving elastic waves propagating in slender structures are numerous. A slender structure can be considered as a waveguide, infinite in one or more directions (plates, bars, tubes ...). Guided waves have the particularity of propagating over long distances with little loss of energy, which can constitute an advantage or a disadvantage depending on the targeted application (non-destructive evaluation vs. reduction of vibrations, for example).One difficulty associated with guided waves is that they are multimodal and dispersive in nature. To determine the behavior of these waves, modeling tools are essential. My research works have been oriented towards the development of generic tools, capable of handling complex geometries. Such modeling tools requires numerical methods. They are based on finite element methods allowing the computation of modes in waveguides with a cross-section, or a unit cell, of arbitrary shape. The developments, theoretical or numerical, take into account various specificities: curvature of waveguides (helical or/and rotational symmetries), excitation, presence of inhomogeneities (local defects), leakage losses (buried waveguides), multi-wire geometry (cables). These five aspects are broken down into different sections that form the outline of the presentation. The overall objective is to take advantage of the modal formalism at every stage: for obtaining the dispersion curves (free response), for the calculation of solutions under excitation (forced response) or for the resolution of diffraction problems (interaction between waves and local inhomogeneities).Among the perspectives of this work, we can cite the development of imaging methods using sensitivity methods. The proposed modeling tools make it possible to exploit the power of modal formalism to quickly calculate solutions to a given excitation (direct and adjoint problems) as well as synthetic data., Les domaines d'applications impliquant des ondes élastiques se propageant dans des structures élancées sont nombreux. Une structure élancée peut être considérée comme un guide d'onde, infini dans une ou plusieurs directions (plaques, barres, tubes...). Les ondes guidées ont la particularité de se propager sur de longues distances avec peu de perte d'énergie, ce qui peut constituer un avantage ou bien un inconvénient suivant l'application visée (évaluation non-destructive vs. réduction des vibrations, par exemple). Une difficulté liée aux ondes guidées est qu'elles sont de nature multimodale et dispersive. Pour déterminer le comportement de ces ondes, des outils de modélisation sont indispensables. Mes travaux se sont orientés vers le développement d'outils généraux, capables de traiter des géométries de guides complexes, ce qui nécessite la mise en oeuvre de méthodes numériques. Les outils mis en place sont basés sur des méthodes d'éléments finis permettant le calcul des modes d'onde. Ils permettent d'étudier des guides ayant une section, ou une cellule unitaire, de forme arbitraire. Les développements, théoriques ou numériques, tiennent compte de diverses spécificités : courbure du guide (symétries hélicoïdales ou/et de rotation), excitation, présence d'inhomogénéités («défauts»), pertes par fuite (enfouissement), géométrie multi-brins (câbles). Ces cinq aspects sont déclinés tour à tour en différentes sections qui forment le plan de l'exposé. L'objectif global est de tirer parti du formalisme modal, que ce soit pour l'obtention des courbes de dispersion (réponses libres), le calcul de solutions sous excitation (réponses forcées) ou pour la résolution de problèmes de diffraction (interaction entre ondes et inhomogénéité locale). Parmi les perspectives envisagées de ces travaux, on peut citer le développement de méthodes d'imagerie par méthodes de sensibilité. Les outils de modélisation proposés permettent en effet d'exploiter la puissance du formalisme modale pour calculer rapidement des solutions à une excitation donnée (problèmes directs et adjoints) ainsi que des données synthétiques.

The fields of applications involving elastic waves propagating in slender structures are numerous. A slender structure can be considered as a waveguide, infinite in one or more directions (plates, bars, tubes ...). Guided waves have the particularity of propagating over long distances with little loss of energy, which can constitute an advantage or a disadvantage depending on the targeted application (non-destructive evaluation vs. reduction of vibrations, for example).One difficulty associated with guided waves is that they are multimodal and dispersive in nature. To determine the behavior of these waves, modeling tools are essential. My research works have been oriented towards the development of generic tools, capable of handling complex geometries. Such modeling tools requires numerical methods. They are based on finite element methods allowing the computation of modes in waveguides with a cross-section, or a unit cell, of arbitrary shape. The developments, theoretical or numerical, take into account various specificities: curvature of waveguides (helical or/and rotational symmetries), excitation, presence of inhomogeneities (local defects), leakage losses (buried waveguides), multi-wire geometry (cables). These five aspects are broken down into different sections that form the outline of the presentation. The overall objective is to take advantage of the modal formalism at every stage: for obtaining the dispersion curves (free response), for the calculation of solutions under excitation (forced response) or for the resolution of diffraction problems (interaction between waves and local inhomogeneities).Among the perspectives of this work, we can cite the development of imaging methods using sensitivity methods. The proposed modeling tools make it possible to exploit the power of modal formalism to quickly calculate solutions to a given excitation (direct and adjoint problems) as well as synthetic data.; Les domaines d'applications impliquant des ondes élastiques se propageant dans des structures élancées sont nombreux. Une structure élancée peut être considérée comme un guide d'onde, infini dans une ou plusieurs directions (plaques, barres, tubes...). Les ondes guidées ont la particularité de se propager sur de longues distances avec peu de perte d'énergie, ce qui peut constituer un avantage ou bien un inconvénient suivant l'application visée (évaluation non-destructive vs. réduction des vibrations, par exemple). Une difficulté liée aux ondes guidées est qu'elles sont de nature multimodale et dispersive. Pour déterminer le comportement de ces ondes, des outils de modélisation sont indispensables. Mes travaux se sont orientés vers le développement d'outils généraux, capables de traiter des géométries de guides complexes, ce qui nécessite la mise en oeuvre de méthodes numériques. Les outils mis en place sont basés sur des méthodes d'éléments finis permettant le calcul des modes d'onde. Ils permettent d'étudier des guides ayant une section, ou une cellule unitaire, de forme arbitraire. Les développements, théoriques ou numériques, tiennent compte de diverses spécificités : courbure du guide (symétries hélicoïdales ou/et de rotation), excitation, présence d'inhomogénéités («défauts»), pertes par fuite (enfouissement), géométrie multi-brins (câbles). Ces cinq aspects sont déclinés tour à tour en différentes sections qui forment le plan de l'exposé. L'objectif global est de tirer parti du formalisme modal, que ce soit pour l'obtention des courbes de dispersion (réponses libres), le calcul de solutions sous excitation (réponses forcées) ou pour la résolution de problèmes de diffraction (interaction entre ondes et inhomogénéité locale). Parmi les perspectives envisagées de ces travaux, on peut citer le développement de méthodes d'imagerie par méthodes de sensibilité. Les outils de modélisation proposés permettent en effet d'exploiter la puissance du formalisme modale pour calculer rapidement des solutions à une excitation donnée (problèmes directs et adjoints) ainsi que des données synthétiques.

This article deals with the dynamic response of laterally unbounded, horizontally layered plates subjected to dynamic sources applied at arbitrary locations, which is ultimately a classical problem. This response is most often obtained via a modal superposition in terms of the complex Lamb modes by casting the equations in the frequency–space domain, followed by a Fourier inversion into the space–time domain. Then again, a much less often used alternative method relies on formulating the problem directly in the time domain in terms of a modal superposition in the wavenumber domain, which is followed by a Fourier inversion into the space–domain, as considered in further detail herein. This alternative can offer powerful advantages in some cases, such as dealing easily with anisotropy, or with slowly propagating waves even in the absence of damping. At the same time, however, it is beset by difficulties associated with the Fourier inversion into the space–domain. As a matter of fact, during forcing, the truncation of the modal series and of the numerical integrals is hindered by poorly convergent behaviors. Here we overcome both of these difficulties by considering the asymptotic, static behavior of the integrands. We find that by introducing a regularizing term, the response can be effectively separated into near and far fields, despite the fact that these frequency-domain concepts are alien to a wavenumber–time formulation. The so-defined far field is free of sharp variations and can then be computed in a numerical grid that is optimized regarding the propagating wavelengths, which only depend on the time-spectral content of the excitation and not on its space-spectrum. Finally, we also propose a hybrid way to compute the remaining near field by combining with a non-modal formulation, expressed in the wavenumber–Laplace domain.

The spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous sample with localized damage [1]. The influence of a strong pump wave on a localized nonlinear damage zone is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. The local change of the elastic modulus and the attenuation coefficient have been shown to vary linearly with respect to the excitation amplitude of the pump wave as in previous experimental studies of Zhang et al. [2]. In this study, the boundary conditions of the cracks, i.e. clapping effects is taken into account in the modeling of the damaged zone. The EDZ is then modeled with random cracks of random orientations, new parametric studies are established to model the pump wave influence with two new parameters: the change of the crack length and the crack density. The numerical results reported constitute another step towards quantification and forecasting of the nonlinear acoustic response of a cracked material, which proves to be necessary for quantitative non-destructive evaluation.The spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous sample with localized damage [1]. The influence of a strong pump wave on a localized nonlinear damage zone is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. The local change of the elastic modulus and the attenuation coefficient have been shown to vary linearly with respect to the excitation amplitude of the pump wave as in previous experimental studies of Zhang et al. [2]. In this study, the boundary conditions of the cracks, i.e. clapping effects is taken into account in the modeling of the damaged zone. The EDZ is then modeled with random cracks of random orientations, new parametric studies are established to model the pump wave influence with two new parameters: the change of the crack length and the crack density. The numerical results reported constitute another step towards...

In this paper, the spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous or heterogeneous sample with localized damage. The influence of a strong pump wave on localized nonlinear damage is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. These modifications are quantified with coda wave interferometry through an overall wave velocity variation probed by a reverberated or multiple scattered coda wave. Results demonstrate that the NCWI observables are independent of the source/receiver positions. Also, relations between the EDZ parameters and method observables are established, e.g. the relative velocity variation is found to be proportional to the product of the change in elastic modulus and the EDZ area. The numerical results reported constitute another step towards quantification and forecasting of the nonlinear acoustic response of a cracked material, which proves to be necessary for a quantitative non-destructive evaluation. Furthermore, it is shown numerically that NCWI sensitivity and applicability are similar for the cases of reverberated waves in a cavity and multiply scattered waves in a heterogeneous medium.