HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perflectly matched layer methodsKhac-Long Nguyen, Fabien Treyssede, Christophe Hazard To cite this version:Khac-Long Nguyen, Fabien Treyssede, Christophe Hazard. Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perflectly matched layer methods. AbstractAmong the numerous techniques of non destructive evaluation, elastic guided waves are of particular interest to evaluate defects inside industrial and civil elongated structures owing to their ability to propagate over long distances. However for guiding structures buried in large solid media, waves can be strongly attenuated along the guide axis due to the energy radiation into the surrounding medium, usually considered as unbounded. Hence, searching the less attenuated modes become necessary in order to maximize the inspection distance. In the numerical modeling of embedded waveguides, the main difficulty is to account for the unbounded section. This paper presents a numerical approach combining a semi-analytical finite element method and a perfectly matched layer (PML) technique to compute the so-called trapped and leaky modes in three-dimensional embedded elastic waveguides of arbitrary cross-section. Two kinds of PML, namely the Cartesian PML and the radial PML, are considered. In order to understand the various spectral objects obtained by the method, the PML parameters effects upon the eigenvalue spectrum are highlighted through analytical studies and numerical experiments. Then, dispersion curves are computed for test cases taken from the literature in order to validate the approach.energy is confined into the core of waveguides without energy leakage into the surrounding medium allowing long inspection distances. Nevertheless, trapped modes do not always occur. For scalar open waveguides (characterized by a scalar field such as the acoustic pressure or the SH wave displacement), trapped modes exist only if the bulk velocity in the core is lower than in the surrounding medium [3]. In the elastic case, both compressional and shear bulk waves occur and, unless Stoneley waves are allowed on the interface between materials, no trapped modes are present when the shear velocity is faster in the core [4,5]. Unfortunately, such a configuration is often encountered in civil structures because the guiding structures are usually embedded in soft solid media such as concr...

Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. In numerous applications, the guiding structure is surrounded by a solid matrix that can be considered as unbounded in the transverse directions. The physics of waves in such an open waveguide significantly differs from a closed waveguide, i.e. for a bounded cross-section. Except for trapped modes, part of the energy is radiated in the surrounding medium, yielding attenuated modes along the axis called leaky modes. These leaky modes have often been considered in non destructive testing applications, which require waves of low attenuation in order to maximize the inspection distance. The main difficulty with numerical modeling of open waveguides lies in the unbounded nature of the geometry in the transverse direction. This difficulty is particularly severe due to the unusual behavior of leaky modes: while attenuating along the axis, such modes exponentially grow along the transverse direction. A simple numerical procedure consists in using absorbing layers of artificially growing viscoelasticity, but large layers may be required. The goal of this paper is to explore another approach for the computation of trapped and leaky modes in open waveguides. The approach combines the so-called semi-analytical finite element method and a perfectly matched layer technique. Such an approach has already been successfully applied in scalar acoustics and electromagnetism. It is extended here to open elastic waveguides, which raises specific difficulties. In this paper, two-dimensional stratified waveguides are considered. As it reveals a rich structure, the numerical eigenvalue spectrum is analyzed in a first step. This allows to clarify the spectral objects calculated with the method, including radiation modes, and their dependency on the perfectly matched layer parameters. In a second step, numerical dispersion curves of trapped and leaky modes are compared to analytical results.

The drilling operations use a rotary slender structure introduced inside the drill well. The nonlinear dynamics with bit-bouncing, stick-slip phenomena, and pulsating mud flow may yield the premature wear and damage of drilling equipment and should be investigated to improve the reliability of drilling operations. This work presents the beam element formulation to model the drilling nonlinear dynamics. The well-pipe contacts are modeled by the radial elastic stops. The fluid–structure interactions are considered. The first step consists in computing the static position of structure to determine the contact points and calculate the preloaded state. These results are then considered to calculate the Campbell diagram. The potentially unstable speeds of rotation are identified. The results show that the modal coupling phenomena strongly occur for the three-dimensional well. The well-pipe contacts modify the modes in rotation, and the rotating fluid induces a strong deviation of the flexural mode curves.

In rotary drilling, a drillstring is an assembly of slender pipes. It is used to transmit the driving torque of a motor at the drilling surface to the drill bit at the bottom hole of a 3D well. Numerous vibratory phenomena are induced during the drilling: whirling, stick-slip, bit-bouncing, lateral instability, inducing in particular reduction of the rate of penetration and mean time between failures. For the rotordynamics prediction of such a structure, the drillpipes are modelled with Timoshenko beam elements, containing 12 degrees of freedom, equipped with distributed radial stop-ends. The rotary motion is assumed to have a constant speed of rotation imposed at the top of the drillstring. The drilling mud is taken into account by using a fluid-structure interaction model. The numerical simulations concern a real 3D-borehole and a parametric analysis is carried out for determining the role of the mud density and of the flows rate on the drillstring dynamics. It is shown that increasing the flow rate and densifying the drilling fluid reduce the fluid damping effect that increases drillstring lateral vibrations.