Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I Formal solution

2005 ◽  
Vol 461 (2063) ◽  
pp. 3413-3436 ◽  
Author(s):  
Ian Thompson ◽  
I. David Abrahams
Keyword(s):  
Formal Solution ◽  
Plane Waves ◽  
Flexural Wave ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Incident Plane ◽  
Principal Directions ◽  
Orthotropic Thin Plate ◽  
Non Destructive ◽  
Kirchhoff Theory

The problem of flexural wave diffraction by a semi-infinite crack in an infinite orthotropic thin plate is considered. Such models have application to the ultrasonic non-destructive inspection of thin components, such as aeroplane wings. For simplicity, the plate is modelled using Kirchhoff theory, and the crack is chosen to be aligned along one of the principal directions of material orthotropy. For incident plane waves, an exact analytical expression for the scattered field is derived by means of the Wiener–Hopf technique. In this model problem, the Wiener–Hopf kernel is scalar and its factorization is expressed in terms of simple, definite, non-singular contour integrals. A detailed numerical evaluation of the solution will be provided in the second part of this work.

Diffraction of flexural waves by cracks in orthotropic thin elastic plates. Part II. Far field analysis

2007 ◽  
Vol 463 (2082) ◽  
pp. 1615-1638 ◽  
Author(s):  
Ian Thompson ◽  
I.David Abrahams
Keyword(s):  
Thin Plate ◽  
Scattered Field ◽  
Asymptotic Approximation ◽  
Principal Direction ◽  
Field Analysis ◽  
Flexural Wave ◽  
Far Field ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Thin Elastic Plates

The scattered field arising from diffraction of a plane flexural wave by a semi-infinite crack in an orthotropic Kirchhoff thin plate is analysed. The crack is aligned with a principal direction of the material, so that two of the plate's three planes of symmetry are preserved. An asymptotic approximation is derived via the method of steepest descents, and explicit expressions are given for the most significant contributions. The effects of anisotropy upon the scattered field are made clear, and numerical results are presented for several typical engineering materials.

Transmission, trapping and filtering of waves in periodically constrained elastic plates

2011 ◽  
Vol 468 (2137) ◽  
pp. 76-93 ◽  
Author(s):  
S. G. Haslinger ◽  
N. V. Movchan ◽  
A. B. Movchan ◽  
R. C. McPhedran
Keyword(s):  
Plane Waves ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Quality Factors ◽  
Reflection And Transmission ◽  
Recurrence Algorithm ◽  
Transmission Resonances ◽  
Scattered Fields ◽  
Induced Transparency ◽  
Suppression Region

The paper discusses properties of flexural waves in elastic plates constrained periodically by rigid pins. A structured interface consists of rigid pin platonic gratings parallel to each other. Although the gratings have the same periodicity, relative shifts in horizontal and vertical directions are allowed. We develop a recurrence algorithm for constructing reflection and transmission matrices required to characterize the filtering of plane waves by the structured interface with shifted gratings. The representations of scattered fields contain both propagating and evanescent terms. Special attention is given to the analysis of trapped modes which may exist within the system of rigid pin gratings. Analytical findings are accompanied by numerical examples for systems of two and three gratings. We show geometries containing three gratings in which transmission resonances have very high quality factors (around 35 000). We also show that controlled lateral shifts of three gratings can give rise to a transmission peak with a sharp central suppression region, akin to the phenomenon of electromagnetic-induced transparency.

Flexural waves in structured elastic plates: Mindlin versus bi-harmonic models

2010 ◽  
Vol 467 (2127) ◽  
pp. 869-880 ◽  
Author(s):  
N. V. Movchan ◽  
R. C. McPhedran ◽  
A. B. Movchan
Keyword(s):  
Band Gap ◽  
Periodic Structures ◽  
Low Frequency ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Floquet Waves ◽  
Plate Models ◽  
Doubly Periodic Array ◽  
Kirchhoff Theory ◽  
Kirchhoff Model

The paper presents an analytical approach to modelling of Bloch–Floquet waves in structured Mindlin plates. The emphasis is given to a comparative analysis of two simplified plate models: the classical Kirchhoff theory and the Mindlin theory for dynamic response of periodic structures. It is shown that in the case of a doubly periodic array of cavities with clamped boundaries, the structure develops a low-frequency band gap in its dispersion diagram. In the framework of the Kirchhoff model, this band gap persists, even when the radius of the cavities tends to zero. A clear difference is found between the predictions of Kirchhoff and Mindlin theories. In Mindlin theory, the lowest band goes down to ω = 0 as the radius of the cavities tends to zero, which is linked with the contrasting behaviour of the corresponding Green functions.

scholarly journals Localization of Scattering Objects Using Neural Networks

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 11
Author(s):  
Domonkos Haffner ◽  
Ferenc Izsák
Keyword(s):  
Neural Networks ◽  
Plane Waves ◽  
Measurement Data ◽  
Scattered Wave ◽  
Training Data ◽  
Data Set ◽  
Main Compound ◽  
Incident Plane ◽  
The Neural Networks ◽  
Simulation Package

The localization of multiple scattering objects is performed while using scattered waves. An up-to-date approach: neural networks are used to estimate the corresponding locations. In the scattering phenomenon under investigation, we assume known incident plane waves, fully reflecting balls with known diameters and measurement data of the scattered wave on one fixed segment. The training data are constructed while using the simulation package μ-diff in Matlab. The structure of the neural networks, which are widely used for similar purposes, is further developed. A complex locally connected layer is the main compound of the proposed setup. With this and an appropriate preprocessing of the training data set, the number of parameters can be kept at a relatively low level. As a result, using a relatively large training data set, the unknown locations of the objects can be estimated effectively.

Fast and slow interaction of elastic waves with platonic clusters

2011 ◽  
Vol 467 (2136) ◽  
pp. 3509-3529 ◽  
Author(s):  
Michael H. Meylan ◽  
Ross C. McPhedran
Keyword(s):  
Elastic Waves ◽  
Early Time ◽  
Approximate Solutions ◽  
Wave Profile ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Analytical Extension ◽  
Scattering Of Elastic Waves ◽  
Classical Models ◽  
The Time Domain

We study the scattering of elastic waves by platonic clusters in the time domain, both for plane wave excitations and for a specified initial wave profile. We show that we can use an analytical extension of our problem to calculate scattering frequencies of the solution. These allow us to calculate approximate solutions that give the flexural wave profile accurately in and around the cluster for large times. We also discuss the early-time behaviour of flexural waves in terms of the classical models of Sommerfeld and Brillouin.

scholarly journals Elastic properties of floating sea ice from air-coupled flexural waves

2021 ◽  
Author(s):  
Rowan Romeyn ◽  
Alfred Hanssen ◽  
Bent Ole Ruud ◽  
Tor Arne Johansen
Keyword(s):  
Sea Ice ◽  
Elastic Properties ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Flexural Wave ◽  
Ice Thickness ◽  
Linear Filter ◽  
Flexural Stiffness ◽  
Flexural Waves ◽  
Impulsive Source

Abstract. Air-coupled flexural waves appear as wave trains of constant frequency that arrive in advance of the direct air-wave from an impulsive source travelling over a floating ice sheet. The frequency of these waves varies with the flexural stiffness of the ice sheet, which is controlled by a combination of thickness and elastic properties. We develop a theoretical framework to understand these waves, utilizing modern numerical and Fourier methods to give a simpler and more accessible description than the pioneering, yet unwieldly analytical efforts of the 1950's. Our favoured dynamical model can be understood in terms of linear filter theory and is closely related to models used to describe the flexural waves produced by moving vehicles on floating plates. We find that air-coupled flexural waves are a robust feature of floating ice-sheets excited by impulsive sources over a large range of thicknesses, and we present a simple closed-form estimator for the ice thickness. Our study is focussed on first-year sea ice of ~20–80 cm thickness in Van Mijenfjorden, Svalbard, that was investigated through active source seismic experiments over four field campaigns in 2013, 2016, 2017 and 2018. The air-coupled flexural frequencies for sea-ice in this thickness range are ~60–240 Hz. While air-coupled flexural waves for thick sea-ice have received little attention, the higher frequencies associated with thin ice on fresh water lakes and rivers are well known to the ice-skating community and have been reported in popular media. Estimation of ice physical properties, following the approach we present, may allow improved surface wave modelling and wavefield subtraction in reflection seismic studies where flexural wave noise is undesirable. On the other hand, air-coupled flexural waves may also permit non-destructive continuous monitoring of ice thickness and flexural stiffness using simple, relatively inexpensive microphones located in the vicinity of the desired measurement location, either above the ice-sheet or along the shoreline. In this case, naturally forming cracks in the ice may be an appropriate impulsive source capable of exciting flexural waves in floating ice sheets in a passive monitoring context.

Quaternion-based anisotropic inversion for flexural waves in horizontal transverse isotropic formations with unmatched sources: A synthetic example

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. A69-A74 ◽  
Author(s):  
Fuqiang Zeng ◽  
Wenzheng Yue ◽  
Chao Li
Keyword(s):  
Structural Information ◽  
Amplitude Ratio ◽  
Flexural Wave ◽  
Data Sets ◽  
Flexural Waves ◽  
P Waves ◽  
Source Type ◽  
Transverse Isotropic ◽  
Sonic Logging ◽  
Incident Waves

The anisotropy of elastic waves has been widely used to obtain structural information on formations in geosciences research. Flexural wave splitting is generally applied to evaluate anisotropy with geophysical inversion methods. Cross-dipole sonic logging has been widely used for anisotropic inversions in horizontal transverse isotropic formations. Traditional methods assume that fast and slow flexural waves are similar in shape and are not dispersive and that the radiation characteristics of the two orthogonal dipole sources are identical. The two above assumptions cannot be satisfied in field conditions. Therefore, the methods used in anisotropy inversion based on these assumptions will lead to inaccurate results. The introduction of the amplitude ratio (AR), the ratio of slow to fast flexural waves, which is not dependent on the source type, can eliminate the wave-shape assumption. Two data sets from orthogonally oriented receivers can be constructed as a quaternion array. Fast and slow flexural waves are the two main incident waves, and other arrivals such as P-waves can be taken as noise. The AR and a quaternion multiple signal classification algorithm are used to demonstrate how to improve the anisotropic inversion and avoid these assumptions. Compared with the traditional method, the new method presents better inversion results for the synthetic example with two different sources. We have determined that the inversion residual from the new objective function can be used to indicate the inversion quality.

scholarly journals Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1656 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Forced Response ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Response Analysis ◽  
Flexural Waves ◽  
Single Wave

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.

scholarly journals Numerical study of the effect of cement defects on flexural-wave logging

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. D171-D177
Author(s):  
Ruolong Song ◽  
Hefeng Dong ◽  
Xueshan Bao
Keyword(s):  
Group Velocity ◽  
Numerical Study ◽  
Staggered Grid ◽  
Flexural Wave ◽  
Burial Depth ◽  
Flexural Waves ◽  
Wave Technique ◽  
Bond Evaluation ◽  
Pulse Echo ◽  
Leaky Lamb Wave

Cement-bond evaluation is needed for new wells and plug and abandonment activities. The ultrasonic leaky Lamb-wave (also called the flexural-wave) technique, in combination with the pulse-echo technique, has been widely used for cement-quality evaluation. Using a 2D time-domain staggered-grid stress-velocity finite-difference methodology, we have numerically investigated the attenuation and group velocity of flexural waves, and the scattering from defects, in the presence of a water-filled void in the cement annulus. The position, length, thickness, and burial depth of a defect are considered. The numerical study suggests that the combination of the attenuation and group velocity of the flexural wave allows for a discrimination between solids and liquids. The scattering from voids can be used to indicate the existence of a hidden defect, which cannot be detected by using the attenuation and group velocity if it is located larger than 5 mm away from the casing. The void signatures can even be used to characterize the geometry of the defect for neat cement. The numerical results provide improved understanding of flexural-wave logging results.

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