Fabien Treyssède

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.

Mode propagation in curved waveguides and scattering by inhomogeneities: Application to the elastodynamics of helical structures

This paper reports on an investigation into the propagation of guided modes in curved waveguides and their scattering by inhomogeneities. In a general framework, the existence of propagation modes traveling in curved waveguides is discussed. The concept of translational invariance, intuitively used for the analysis of straight waveguides, is highlighted for curvilinear coordinate systems. Provided that the cross-section shape and medium properties do not vary along the waveguide axis, it is shown that a sufficient condition for invariance is the independence on the axial coordinate of the metric tensor. Such a condition is indeed checked by helical coordinate systems. This study then focuses on the elastodynamics of helical waveguides. Given the difficulty in achieving analytical solutions, a purely numerical approach is chosen based on the so-called semi-analytical finite element method. This method allows the computation of eigenmodes propagating in infinite waveguides. For the investigation of modal scattering by inhomogeneities, a hybrid finite element method is developed for curved waveguides. The technique consists in applying modal expansions at cross-section boundaries of the finite element model, yielding transparent boundary conditions. The final part of this paper deals with scattering results obtained in free-end helical waveguides. Two validation tests are also performed.

Investigation of the interwire energy transfer of elastic guided waves inside prestressed cables

Elastic guided waves are of interest for the non-destructive evaluation of cables. Cables are most often multi-wire structures, and understanding wave propagation requires numerical models accounting for the helical geometry of individual wires, the interwire contact mechanisms and the effects of prestress. In this paper, a modal approach based on a so-called semi-analytical finite element method and taking advantage of a biorthogonality relation is proposed in order to calculate the forced response under excitation of a cable, multi-wired, twisted, and prestressed. The main goal of this paper is to investigate how the energy transfers from a given wire, directly excited, to the other wires in order to identify some localization of energy inside the active wire as the waves propagate along the waveguide. The power flow of the excited field is theoretically derived and an energy transfer parameter is proposed to evaluate the level of energy localization inside a given wire. Numerical results obtained for different polarizations of excitation, central and peripheral, highlight how the energy may localize, spread, or strongly change in the cross-section as waves travel along the axis. In particular, a compressional mode localized inside the central wire is found, with little dispersion and significant excitability.

Computation of Dispersion Curves in Elastic Waveguides of Arbitrary Cross- section embedded in Infinite Solid Media

Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. However, guiding structures are often buried in a large domain, considered as unbounded. Waveguides are then open and waves can be trapped or leaky. Analytical tools have been developed to model open solid waveguides but these tools are limited for simple geometries (plates, cylinders). With numerical methods, a difficulty is due to the unbounded geometry. Another issue is due to the presence of leaky modes, which grow exponentially along the transverse directions. The goal of this work is to implement a numerical approach to calculate modes in three dimensional elastic open waveguides, which combines the semi-analytical finite element method and the perfectly matched layers (PML) technique. Both Cartesian and cylindrical PML are implemented.

Non destructive evaluation of seven-wire strands using ultrasonic guided waves

ABSTRACT Seven-wire strands are widely used in civil engineering structures for cable-stayed bridges, prestressed concrete bridges or retaining walls applications. Corrosion and fatigue induced damages are of major concern for these metallic strands. The aim of this paper is to give an overview of the theoretical and experimental works on the non destructive evaluation (NDE) of steel members using ultrasonic guided waves generated and detected with piezoelectric or magnetostrictive transducers. Results obtained for different frequency ranges on various configurations will be shown and discussed in order to quantify the performances and limits of guided ultrasonic wave inspection methodologies.

A semianalytical finite element method for elastic guided waves propagating in helical structures

Steel multiwire cables are widely used in civil engineering as load‐carrying members. The basic element of these cables is usually a simple straight strand made of a straight core and one layer of helical wires. Several difficulties arise in the understanding of guided ultrasonic waves in such structures, partly due to the helical geometry and the interwire coupling effects. In the context of nondestructive evaluation, this paper aims at theoretically investigating the propagation of elastic waves in helical waveguides. A numerical method is chosen based on a semianalytical finite element technique that relies on a specific nonorthogonal curvilinear coordinate system. This system is shown to be translationally invariant along the helix centerline so that a spatial Fourier transform can be explicitly performed along the axis and the problem is reduced to two dimensions. A single helical wire is first considered. The convergence and accuracy of the proposed method are assessed by comparing finite element re...

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.

A modal approach based on perfectly matched layers for the forced response of elastic open waveguides

Abstract This paper investigates the computation of the forced response of elastic open waveguides with a numerical modal approach based on perfectly matched layers (PML). With a PML of infinite thickness, the solution can theoretically be expanded as a discrete sum of trapped modes, a discrete sum of leaky modes and a continuous sum of radiation modes related to the PML branch cuts. Yet with numerical methods (e.g. finite elements), the waveguide cross-section is discretized and the PML must be truncated to a finite thickness. This truncation transforms the continuous sum into a discrete set of PML modes. To guarantee the uniqueness of the numerical solution of the forced response problem, an orthogonality relationship is proposed. This relationship is applicable to any type of modes (trapped, leaky and PML modes) and hence allows the numerical solution to be expanded on a discrete sum in a convenient manner. This also leads to an expression for the modal excitability valid for leaky modes. The physical relevance of each type of mode for the solution is clarified through two numerical test cases, a homogeneous medium and a circular bar waveguide example, excited by a point source. The former is favourably compared to a transient analytical solution, showing that PML modes reassemble the bulk wave contribution in a homogeneous medium. The latter shows that the PML mode contribution yields the long-term diffraction phenomenon whereas the leaky mode contribution prevails closer to the source. The leaky mode contribution is shown to remain accurate even with a relatively small PML thickness, hence reducing the computational cost. This is of particular interest for solving three-dimensional waveguide problems, involving two-dimensional cross-sections of arbitrary shapes. Such a problem is handled in a third numerical example by considering a buried square bar.

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.