Laurent Laguerre

Numerical and analytical calculation of modal excitability for elastic wave generation in lossy waveguides

In the analysis of elastic waveguides, the excitability of a given mode is an important feature defined by the displacement-force ratio. Useful analytical expressions have been provided in the literature for modes with real wavenumbers (propagating modes in lossless waveguides). The central result of this paper consists in deriving a generalized expression for the modal excitability valid for modes with complex wavenumbers (lossy waveguides or non-propagating modes). The analysis starts from a semi-analytical finite element method and avoids solving the left eigenproblem. Analytical expressions of modal excitability are then deduced. It is shown that the fundamental orthogonality property to be used indeed corresponds to a form of Aulds real orthogonality relation, involving both positive- and negative-going modes. Finally, some results obtained from the generalized excitability are compared to the approximate lossless expression.

Non-destructive assessment of hot mix asphalt compaction/ density with a step-frequency radar: case study on a newly paved road

A Step-Frequency Radar (SFR) is used for assessing the compaction of Hot Mix Asphalt (HMA) layers. The system is composed of a network analyser and an Ultra Wide Band (UWB) antenna placed above the road surface. The measurements are carried out on a newly paved road in Cagny (Normandy, France). The SFR system provides the permittivity of the first overlay. The data is corrected from vehicle vibrations and calibrated at fixed locations. Then, the HMA compaction is deduced with a Lichtenecker–Rother (LR) model. The results are compared with standard tests (gamma bench testing on cores and in-place nuclear gauge). We show that the SFR system allows the nondestructive assessment of HMA overlay with a high density of points and with accuracy close to the compaction provided by standard tests.

Contribution of leaky modes in the modal analysis of unbounded problems with perfectly matched layers

The modal analysis of wave problems of unbounded type involves a continuous sum of radiation modes. This continuum is difficult to handle mathematically and physically. It can be approximated by a discrete set of leaky modes, corresponding to improper modes growing to infinity. Perfectly matched layers (PMLs) have been widely applied in numerical methods to efficiently simulate infinite media, most often without considering a modal approach. This letter aims to bring insight into the modal basis computed with PMLs. PMLs actually enable to reveal of the contribution of leaky modes by redefining the continua (two for elastodynamics), discretized after PML truncation.

Non destructive assessment of Hot Mix Asphalt compaction with a step frequency radar: Case study

A Step Frequency Radar (SFR) is used for assessing the compaction of Hot Mix Asphalt (HMA) layers. The system is composed of a network analyser and an Ultra Wide Band (UWB) antenna placed above the road surface. The measurements are carried out on a new-paved road in Cagny (Normandie, France). The SFR system provides the permittivity of the first overlay. The data is corrected from vehicle vibrations and calibrated at fixed locations. Then, the HMA compaction is deduced with a Lichteneker-Rother (LR) model. The results are compared with standard tests (gamma bench testing on cores and in-place nuclear gauge). We show that the SFR system allows the nondestructive assessment of HMA overlay with a high density of points, and with an accuracy close to the compaction provided by standard tests.

On the benefits of Debye series for modeling the ultrasonic propagation in a waveguide

This short communication aims to compare the Debye series with a modal series for the case of the propagation of a bounded beam in an embedded waveguide. The calculation can be achieved through several methods. These methods are described briefly and the most preponderant references are given. The Modal Expansion Method which is among these method is compared to the Debye series which is combined with the Integral Transform Method. The benefits of the Debye series for the case of embedded waveguides are highlighted.

Scattering of guided waves from discontinuities in cylinders: Numerical and experimental analysis

The aim of this work is to study the fundamental compressional (L(0,1)) Pochhammer-Chree mode interaction with nonaxisymmetric damages in cylinders. To this end, experimental and numerical investigations of non-axisymmetric vertical cracks are considered. A non-contact magnetostrictive device is used for experimental investigations. Magnetostrictive transducers are used to generate and receive compressional guided waves. These are enabled by using an axisymmetric and longitudinal magnetic polarising field. Both, the incident and the reflected signals are acquired by the same receiver which allows a direct calculation of the reflected power flow. Different vertical cracks with various depths milled in steel cylinders are considered. The power flows are compared with those obtained by a three dimensional numerical method. This numerical method is based on a hybrid three dimensional (3D) approach combining the classical finite element (FE) method with the semi-analytical finite element (SAFE) technique. The ...

Seismic dispersion analysis feasibility for the subgrade investigation: measurement, experimental and numerical modeling

In the construction of roads or railways, the capping layer is the last layer of the earthworks phase. This layer can be made of non bound aggregates or by a treatment of a soil with lime and/or hydraulic binder, such as cement or hydraulic road binders. In the latter case, the in situ testing of the capping layer performances should encompass treated soil modulus measurements, but sampling such materials is not often satisfactory, because of the risk of material degradation by the sampling itself. Consequently, a non destructive method, aiming at measuring the modulus of the treated materials, could be very useful. For this reason, we propose to study the feasibility of the seismic surface or guided waves dispersion analysis in order to recover the depth and the S wave velocity of the subgrade. Previous works provided results and analysis of the dispersion curves concerning the pavement auscultation (Ryden et al, 2004). However, in these cases, the subgrade was an underlying layer in the global zone of interest that includes the upper pavement layers where the measurement surface is the thin asphalt layer. In the present study, we focus on the subgrade layer in the case of under construction roads, before the shallower pavement layers are built because it should help to qualify the project acceptance concerning this earthworks phase. In this context, the issue deals with a two layers medium case where the investigated subgrade, whom the top is the measurement surface, lays above a low velocity zone, i.e. the natural soil. As described by Ryden et al. (2004), the resulting dispersion curves in the case of a high velocity upper layer should be typical of Lamb waves dispersion curves and could bring out higher modes that could be difficult to pick. In this case, they advocated the entire dispersion diagram inversion to avoid any subjective picking in the data (Ryden et al, 2006). However, the treated soil can contain heterogeneities unfavourable to the assumption of homogeneous layers presupposed to the dispersion diagram calculation. Thus a first feasibility stage, i.e. a field experimental data acquisition, was conducted to define the ability of seismic data to provide a coherent dispersion diagram in the spectral content required. The dispersion curve have been extracted and inverted with an iterative weighted least squares local minimization method (Hermann, 2002). In order to consider the possibility of inverting the entire dispersion diagram, a second feasibility stage consisted in analysing all the events that possibly occur in the dispersion diagram. For that, the measurement experience was reproduced at reduced scale in laboratory as a perfectly controlled experimental modelling approach. These data and more precisely the dispersion diagram is compared in one hand to the theoretical curves associated to the leakage attenuations and in an other hand to the theoretical dispersion diagram numerically calculated with an original method taking into account the source effects.