A two‐and‐a‐half‐dimensional displacement‐based PML for elastodynamic wave propagation

François, Stijn; Schevenels, Mattias; Lombaert, Geert; Degrande, Geert

doi:10.1002/nme.3344

Cited by 39 publications

(20 citation statements)

References 32 publications

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“…Note also that the SAFE-CPML formulation of this paper is indeed similar to the 2.5D displacement-based PML formulation recently proposed in Ref. [37] (yet in this reference, the discretized problem was not considered as an eigenvalue problem, but rather inverted by considering a source term for fixed transverse wavenumbers). This paper focuses on the implementation and the validation of the SAFE-PML method.…”

Section: Introductionmentioning

confidence: 73%

Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods

Nguyen¹,

Treyssède²,

Hazard

2015

Journal of Sound and Vibration

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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...

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Section: Introductionmentioning

confidence: 73%

Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods

Nguyen¹,

Treyssède²,

Hazard

2015

Journal of Sound and Vibration

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“…This is illustrated in figure 2. Application of the spatial windowing technique in the framework of the 2.5D FE-BE methodology outlined in subsection 2.2 implies that the contribution of each wavenumber component of the displacement vectorũ s (k y , ω) is distributed over the entire wavenumber domain according to equation (11). The spatially windowed displacement vectorũ s,sw (k y , ω) can hence be expressed as:…”

Section: 5d Coupled Fe-be Methods With Spatial Windowingmentioning

confidence: 99%

“…The efficiency of coupled FE-BE methods is strongly reduced in the case of embedded structures, however, as the Green's functions have to be evaluated for a large number of source/receiver depths for the assembly of the BE matrices. Alternative numerical solution procedures in a 2.5D framework have therefore been formulated as well, such as a 2.5D finite-infinite element approach proposed by Yang et al [9,10] or a 2.5D perfectly matched layer (PML) technique described by François et al [11].…”

Section: Introductionmentioning

confidence: 99%

A spatial windowing technique to account for finite dimensions in 2.5D dynamic soil–structure interaction problems

Coulier¹,

Dijckmans²,

François³

et al. 2014

Soil Dynamics and Earthquake Engineering

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The dynamic interaction between a layered halfspace and quasi translationally invariant structures such as roads, railway tracks, tunnels, dams, and lifelines can be modelled using a computationally efficient 2.5D approach, assuming invariance of the geometry in the longitudinal direction. This assumption is not always fulfilled in practice, however. Even for elongated structures, full 3D computations may be required for an accurate solution of the dynamic soil-structure interaction problem. This paper presents a spatial windowing technique for elastodynamic transmission and radiation problems that allows accounting for the finite length of a structure, still maintaining the computational efficiency of a 2.5D formulation. The proposed technique accounts for the diffraction occurring at the structure's edges, but not for its modal behaviour resulting from reflections of waves at its boundaries. Numerical examples of a barrier for vibration transmission and a surface foundation are discussed to demonstrate the accuracy and applicability of the proposed methodology. Full 3D calculations are performed to provide a rigorous validation for each of these examples. It is demonstrated that the proposed technique is appropriate as long as the response is not dominated by the resonant behaviour of individual modes of the structure.

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“…In order to prevent the results to be affected by the external geometry and boundary conditions, it is suggested to embed the transducer in an infinite medium. This can be achieved with the help of specific elements such as boundary elements, infinite elements, Absorbing Boundary Conditions (ABC) [21,22,[47][48][49] or Perfectly Matched Layers (PML) [23,24,50]. The last two are by far the most widely used methods since they can be easily implemented in a finite element software.…”

Section: Finite Element Model Of Embedded Piezoelectric Transducersmentioning

confidence: 99%

“…Perfectly Matched Layers are unquestionably the most accurate elements since they are known to appropriately absorb compression, shear and surface waves, evanescent and propagating waves, at any angle of incidence [23,24,50]. Their use can lead to heavy computational costs.…”

Section: Finite Element Model Of Embedded Piezoelectric Transducersmentioning

confidence: 99%

Design optimization of embedded ultrasonic transducers for concrete structures assessment

Dumoulin

2017

Ultrasonics

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In the last decades, the field of structural health monitoring and damage detection has been intensively explored. Active vibration techniques allow to excite structures at high frequency vibrations which are sensitive to small damage. Piezoelectric PZT transducers are perfect candidates for such testing due to their small size, low cost and large bandwidth. Current ultrasonic systems are based on external piezoelectric transducers which need to be placed on two faces of the concrete specimen. The limited accessibility of in-service structures makes such an arrangement often impractical. An alternative is to embed permanently low-cost transducers inside the structure. Such types of transducers have been applied successfully for the in-situ estimation of the P-wave velocity in fresh concrete, and for crack monitoring. Up to now, the design of such transducers was essentially based on trial and error, or in a few cases, on the limitation of the acoustic impedance mismatch between the PZT and concrete. In the present study, we explore the working principles of embedded piezoelectric transducers which are found to be significantly different from external transducers. One of the major challenges concerning embedded transducers is to produce very low cost transducers. We show that a practical way to achieve this imperative is to consider the radial mode of actuation of bulk PZT elements. This is done by developing a simple finite element model of a piezoelectric transducer embedded in an infinite medium. The model is coupled with a multi-objective genetic algorithm which is used to design specific ultrasonic embedded transducers both for hard and fresh concrete monitoring. The results show the efficiency of the approach and a few designs are proposed which are optimal for hard concrete, fresh concrete, or both, in a given frequency band of interest.

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A two‐and‐a‐half‐dimensional displacement‐based PML for elastodynamic wave propagation

Cited by 39 publications

References 32 publications

Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods

Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods

A spatial windowing technique to account for finite dimensions in 2.5D dynamic soil–structure interaction problems

Design optimization of embedded ultrasonic transducers for concrete structures assessment

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