On the use of absorbing layers to simulate the propagation of elastic waves in unbounded isotropic media using commercially available Finite Element packages
TL;DR: In this article, the authors address methods to dramatically enhance computational efficiency by only meshing a local region of the material surrounding the defect; this reduction requires some kind of boundary, or boundary condition, which absorbs, rather than reflects, any waves arriving at the exterior of the modeled domain.
Abstract: Finite Element models for simulating wave propagation and scattering from defects are vital for ultrasonic methods in NDE. This article addresses methods to dramatically enhance computational efficiency by only meshing a local region of the material surrounding the defect; this reduction requires some kind of boundary, or boundary condition, which absorbs, rather than reflects, any waves arriving at the exterior of the modelled domain. A variety of approaches exist and we take two approaches, Perfectly Matched Layers (PML) and Absorbing Regions, selected specifically as they are readily implemented in commercially available Finite Element packages without requiring the source code. We illustrate both bulk and guided waves, and analysis is used to guide the performance, and thus to plan the use, of each of them. Finally, application examples illustrate the gains yielded by absorbing layer methods in terms of reducing both model size and unwanted reflections.
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TL;DR: An approach is developed to perform explicit time domain finite element simulations of elastodynamic problems on the graphical processing unit, using Nvidia?s CUDA, significantly faster than an equivalent commercial CPU package.
146 citations
Cites background from "On the use of absorbing layers to s..."
...Such an approach is discussed in detail in [49]....
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TL;DR: In this paper, the authors investigated the potential advantages and disadvantages of using graded resonant devices as energy harvesters and developed accurate models of the phenomena and extended their analysis to that of an elastic half-space and Rayleigh surface waves.
Abstract: In elastic wave systems, combining the powerful concepts of resonance and spatial grading within structured surface arrays enable resonant metasurfaces to exhibit broadband wave trapping, mode conversion from surface (Rayleigh) waves to bulk (shear) waves, and spatial frequency selection. Devices built around these concepts allow for precise control of surface waves, often with structures that are subwavelength, and utilise Rainbow trapping that separates the signal spatially by frequency. Rainbow trapping yields large amplifications of displacement at the resonator positions where each frequency component accumulates. We investigate whether this amplification, and the associated control, can be used to create energy harvesting devices; the potential advantages and disadvantages of using graded resonant devices as energy harvesters is considered. We concentrate upon elastic plate models for which the A 0 mode dominates, and take advantage of the large displacement amplitudes in graded resonant arrays of rods, to design innovative metasurfaces that trap waves for enhanced piezoelectric energy harvesting. Numerical simulation allows us to identify the advantages of such graded metasurface devices and quantify its efficiency, we also develop accurate models of the phenomena and extend our analysis to that of an elastic half-space and Rayleigh surface waves.
101 citations
TL;DR: A modified Lysmer–Kuhlemeyer approach to be used in the NRB design for Lamb wave problems is proposed, which can be effectively and conveniently implemented in commercial finite element (FE) codes.
90 citations
Cites background from "On the use of absorbing layers to s..."
...But discrepancies have been reported in elastic wave scattering problemswhen both the pressure and shear wavemodes are present [6,7]....
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TL;DR: A Stiffness Reduction Method (SRM) has been developed that operates within a significantly reduced spatial domain, and has been shown to perform significantly better than ALID, with results confirmed by both numerical and analytical means.
68 citations
TL;DR: In this paper, the authors present a systematic analysis of the defect detection performance of each method with sharp and gradual defects, as well as their sensitivity to attenuative coatings, liquid loading, surface roughness and ability to test beyond features such as T-joints.
Abstract: Inspection for corrosion and pitting defects in the petrochemical industry is vital and forms a significant fraction of the operating expenditure. Low frequency guided wave inspection is frequently employed as it gives large area coverage from a single transducer position. However, detection becomes problematic at inaccessible regions such as pipe supports or beyond T-joints since the low frequency guided waves produce a significant reflection from the feature itself, hence limiting the defect detectability of the method. This suggests testing at higher frequencies which helps to minimise the reflection from the feature and also improves the sensitivity to smaller defects. There are a number of guided wave and related techniques implemented for corrosion inspection including the S0 mode (at ∼ 1 MHz-mm), SH0 and SH1 modes (at ∼ 3 MHz-mm), CHIME, M-skip and Higher Order Mode Cluster (A1 mode at ∼ 18 MHz-mm). This paper presents a systematic analysis of the defect detection performance of each method with sharp and gradual defects, as well as their sensitivity to attenuative coatings, liquid loading, surface roughness and ability to test beyond features such as T-joints. It is shown by finite element analysis backed up by experiments that the A1 mode provides the best overall performance when dealing with surface features such as T-joints and coatings because of its low surface motion. Additionally a combination of two or more methods is suggested for corrosion inspection at inaccessible locations: The A1 mode in reflection for severe, sharp, pitting type defects; long range guided waves in reflection for large-area thinning and the SH1 mode in transmission for shallow, gradual defects.
67 citations
Cites methods from "On the use of absorbing layers to s..."
...In FE, the water boundary was generated using AC2D4R elements which are acoustic elements that do not support shear waves; these elements were appropriately tied to the surface of the plate and to mimic a semi-infinite space of water, Absorbing Layers using Increasing Damping (ALID) [48] elements were placed adjacent to the acoustic element layer to absorb the leaked energy and prevent it from re-entering the plate structure....
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TL;DR: Numerical experiments and numerical comparisons show that the PML technique works better than the others in all cases; using it allows to obtain a higher accuracy in some problems and a release of computational requirements in some others.
9,875 citations
TL;DR: In this article, a sequence of radiating boundary conditions is constructed for wave-like equations, and it is proved that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r exp -m-1/2) for the m-th boundary condition.
Abstract: In the numerical computation of hyperbolic equations it is not practical to use infinite domains; instead, the domain is truncated with an artificial boundary. In the present study, a sequence of radiating boundary conditions is constructed for wave-like equations. It is proved that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r exp -m-1/2) for the m-th boundary condition. Numerical experiments with problems in jet acoustics verify the practical nature of the boundary conditions.
999 citations
TL;DR: This paper presents a review of the main developments of the matrix techniques, and their use in response and modal models, with emphasis on ultrasonics applications.
Abstract: Research into ultrasonic NDE techniques for the inspection of multilayered structures relies strongly on the use of modeling tools which calculate dispersion curves and reflection and transmission spectra. These predictions are essential to enable the best inspection strategies to be identified and their sensitivities to be evaluated. General purpose multilayer modeling tools may be developed from a number of matrix formulations which have evolved in the latter half of this century and there is now a formidable number of publications on the subject. This paper presents a review of the main developments of the matrix techniques, and their use in response and modal models, with emphasis on ultrasonics applications. >
931 citations
TL;DR: In this article, a two-dimensional Fourier transform (2D FFT) was used to measure the amplitudes and velocities of the Lamb waves propagating in a plate, the output of the transform being presented using an isometric projection which gives a three-dimensional view of the wave-number dispersion curves.
Abstract: A technique for the analysis of propagating multimode signals is presented. The method involves a two-dimensional Fourier transformation of the time history of the waves received at a series of equally spaced positions along the propagation path. The technique has been used to measure the amplitudes and velocities of the Lamb waves propagating in a plate, the output of the transform being presented using an isometric projection which gives a three-dimensional view of the wave-number dispersion curves. The results of numerical and experimental studies to measure the dispersion curves of Lamb waves propagating in 0.5-, 2.0-, and 3.0-mm-thick steel plates are presented. The results are in good agreement with analytical predictions and show the effectiveness of using the two-dimensional Fourier transform (2-D FFT) method to identify and measure the amplitudes of individual Lamb modes.
889 citations
TL;DR: In this article, a technique for developing radiating boundary conditions for artificial computational boundaries is described and applied to a class of problems typical in exploration seismology involving acoustic and elastic wave equations.
Abstract: A technique for developing radiating boundary conditions for artificial computational boundaries is described and applied to a class of problems typical in exploration seismology involving acoustic and elastic wave equations. First, one considers a constant coefficient scalar wave equation where the artificial boundary is one edge of a rectangular domain. By using continued fraction expansions, a systematic sequence of stable highly absorbing boundary conditions with successively better absorbing properties as the order of the boundary conditions increases is obtained. There follows a systematic derivation of a hierarchy of local radiating boundary conditions for the elastic wave equation. A theoretical procedure to guarantee stability at corners of the rectangular domain is worked out. A technique for fitting the discrete radiating boundary conditions directly to the difference scheme itself is proposed.
780 citations