Scattering of flexural waves by an inhomogeneity in a thin plate
The characteristics of defects in plate-like structures can be extracted from the scattered flexural waves. The scattering of flexural waves is studied in this paper, using the integral equation method in the framework of the Mindlin plate theory. Using the Born approximation, the expression for the...
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| Published in | Wave motion Vol. 75; pp. 50 - 61 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.12.2017
Elsevier BV |
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| Abstract | The characteristics of defects in plate-like structures can be extracted from the scattered flexural waves. The scattering of flexural waves is studied in this paper, using the integral equation method in the framework of the Mindlin plate theory. Using the Born approximation, the expression for the flexural waves scattered by an inhomogeneity can be obtained, in which the Hankel function, rather than the exponential function, is involved in the integral kernel. Therefore, the far-field assumptions for the scatterer are not needed. The closed form for the singular integration of the Hankel function is solved, and hence, the complete scattered field near as well as inside the scatter can be calculated. The effective range of the far-field approximation is obtained by investigating the scattering amplitude of a circular inhomogeneity. In the case where the inhomogeneity diameter (2a) is less than one wavelength (λ), the far-field approximation achieves an accuracy of 1% at a distance greater than 2λ. If the inhomogeneity diameter is larger than λ, 1% accuracy will be achieved by the far-field approximation at a distance greater than 3ka.
•The singular integration of Hankel function at R=0 is solved and the field inside the scatter can also be calculated.•Effective range of far-field approximation is investigated quantitatively. |
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| AbstractList | The characteristics of defects in plate-like structures can be extracted from the scattered flexural waves. The scattering of flexural waves is studied in this paper, using the integral equation method in the framework of the Mindlin plate theory. Using the Born approximation, the expression for the flexural waves scattered by an inhomogeneity can be obtained, in which the Hankel function, rather than the exponential function, is involved in the integral kernel. Therefore, the far-field assumptions for the scatterer are not needed. The closed form for the singular integration of the Hankel function is solved, and hence, the complete scattered field near as well as inside the scatter can be calculated. The effective range of the far-field approximation is obtained by investigating the scattering amplitude of a circular inhomogeneity. In the case where the inhomogeneity diameter (2α) is less than one wavelength (λ), the far-field approximation achieves an accuracy of 1% at a distance greater than 2λ. If the inhomogeneity diameter is larger than λ, 1% accuracy will be achieved by the far-field approximation at a distance greater than 3κα. The characteristics of defects in plate-like structures can be extracted from the scattered flexural waves. The scattering of flexural waves is studied in this paper, using the integral equation method in the framework of the Mindlin plate theory. Using the Born approximation, the expression for the flexural waves scattered by an inhomogeneity can be obtained, in which the Hankel function, rather than the exponential function, is involved in the integral kernel. Therefore, the far-field assumptions for the scatterer are not needed. The closed form for the singular integration of the Hankel function is solved, and hence, the complete scattered field near as well as inside the scatter can be calculated. The effective range of the far-field approximation is obtained by investigating the scattering amplitude of a circular inhomogeneity. In the case where the inhomogeneity diameter (2a) is less than one wavelength (λ), the far-field approximation achieves an accuracy of 1% at a distance greater than 2λ. If the inhomogeneity diameter is larger than λ, 1% accuracy will be achieved by the far-field approximation at a distance greater than 3ka. •The singular integration of Hankel function at R=0 is solved and the field inside the scatter can also be calculated.•Effective range of far-field approximation is investigated quantitatively. |
| Author | Lu, Laiyu |
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| Cites_doi | 10.1121/1.1739482 10.2514/3.2716 10.1046/j.1365-246x.2001.01460.x 10.1016/j.wavemoti.2007.05.005 10.1016/S0165-2125(97)00016-4 10.1121/1.3277217 10.1190/1.1440527 10.1006/jsvi.1995.0129 10.1016/j.jsv.2004.02.023 10.1121/1.3533742 10.1121/1.3533741 10.1016/j.jsv.2009.10.017 10.1016/j.jsv.2012.06.002 10.1111/j.1365-246X.2008.03787.x |
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| Keywords | 99-00 Near-field effect 00-01 Flexural wave Scattering Singular integration Mindlin plate |
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| References | Lu, Maupin, Zeng, Ding (b12) 2008; 174 Vemula, Norris (b4) 1997; 26 Hohmann (b13) 1975; 40 Gradshteyn, Ryzhik (b15) 2007 Ng, Veidt (b8) 2011; 129 Abramowitz, Stegun (b14) 1972 Veidt, Ng (b16) 2011; 129 Norris, Vemula (b3) 1995; 181 Pao, Chao (b2) 1964; 2 Maupin (b11) 2001; 146 Cegla, Rohde, Veidt (b5) 2008; 45 Rose, Wang (b1) 2004; 116 Wang, Chang (b10) 2005; 282 Lee, Chen (b6) 2010; 329 Ng, Veidt, Rose, Wang (b9) 2012; 331 Rose, Wang (b7) 2010; 127 Maupin (10.1016/j.wavemoti.2017.08.006_b11) 2001; 146 Cegla (10.1016/j.wavemoti.2017.08.006_b5) 2008; 45 Norris (10.1016/j.wavemoti.2017.08.006_b3) 1995; 181 Wang (10.1016/j.wavemoti.2017.08.006_b10) 2005; 282 Veidt (10.1016/j.wavemoti.2017.08.006_b16) 2011; 129 Ng (10.1016/j.wavemoti.2017.08.006_b9) 2012; 331 Lee (10.1016/j.wavemoti.2017.08.006_b6) 2010; 329 Vemula (10.1016/j.wavemoti.2017.08.006_b4) 1997; 26 Hohmann (10.1016/j.wavemoti.2017.08.006_b13) 1975; 40 Gradshteyn (10.1016/j.wavemoti.2017.08.006_b15) 2007 Lu (10.1016/j.wavemoti.2017.08.006_b12) 2008; 174 Ng (10.1016/j.wavemoti.2017.08.006_b8) 2011; 129 Pao (10.1016/j.wavemoti.2017.08.006_b2) 1964; 2 Rose (10.1016/j.wavemoti.2017.08.006_b7) 2010; 127 Abramowitz (10.1016/j.wavemoti.2017.08.006_b14) 1972 Rose (10.1016/j.wavemoti.2017.08.006_b1) 2004; 116 |
| References_xml | – volume: 174 start-page: 857 year: 2008 end-page: 872 ident: b12 article-title: Scattering of surface waves modelled by the integral equation method publication-title: Geophys. J. Int. contributor: fullname: Ding – volume: 129 start-page: 1280 year: 2011 end-page: 1287 ident: b16 article-title: Influence of stacking sequence on scattering characteristics of the fundamental anti-symmetric lamb wave at through holes in composite laminates publication-title: J. Acoust. Soc. Am. contributor: fullname: Ng – volume: 2 start-page: 2004 year: 1964 end-page: 2010 ident: b2 article-title: Diffraction of flexural waves by a cavity in an elastic plate publication-title: J. AIAA contributor: fullname: Chao – volume: 26 start-page: 1 year: 1997 end-page: 12 ident: b4 article-title: Flexural wave propagation and scattering on thin plates using Mindlin theory publication-title: Wave Motion contributor: fullname: Norris – year: 1972 ident: b14 article-title: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables contributor: fullname: Stegun – volume: 45 start-page: 162 year: 2008 end-page: 177 ident: b5 article-title: Analytical prediction and experimental measurement for mode conversion and scattering of plate waves at non-symmetric circular blind holes in isotropic plates publication-title: Wave Motion contributor: fullname: Veidt – volume: 127 start-page: 754 year: 2010 end-page: 763 ident: b7 article-title: Mindlin plate theory for damage detection: Imaging of flexural inhomogeneities publication-title: J. Acoust. Soc. Am. contributor: fullname: Wang – volume: 331 start-page: 4870 year: 2012 end-page: 4883 ident: b9 article-title: Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates publication-title: J. Sound Vib. contributor: fullname: Wang – volume: 116 start-page: 154 year: 2004 end-page: 171 ident: b1 article-title: Mindlin plate theory for damage detection: Source solutions publication-title: J. Acoust. Soc. Am. contributor: fullname: Wang – volume: 181 start-page: 115 year: 1995 end-page: 125 ident: b3 article-title: Scattering of flexural waves on thin plates publication-title: J. Sound Vib. contributor: fullname: Vemula – volume: 146 start-page: 332 year: 2001 end-page: 348 ident: b11 article-title: A multiple-scattering scheme for modelling surface wave propagation in isotropic and anisotropic three-dimensional structures publication-title: Geophys. J. Int. contributor: fullname: Maupin – volume: 40 start-page: 309 year: 1975 end-page: 324 ident: b13 article-title: Three-dimensional induced polarization and electromagnetic modeling publication-title: Geophysics contributor: fullname: Hohmann – year: 2007 ident: b15 article-title: Table of Integrals, Series, and Products contributor: fullname: Ryzhik – volume: 129 start-page: 1288 year: 2011 end-page: 1296 ident: b8 article-title: Scattering of the fundamental anti-symmetric Lamb wave at delaminations in composite laminates publication-title: J. Acoust. Soc. Am. contributor: fullname: Veidt – volume: 329 start-page: 1042 year: 2010 end-page: 1061 ident: b6 article-title: Scattering of flexural wave in a thin plate with multiple circular inclusions by using the null-field integral equation approach publication-title: J. Sound Vib. contributor: fullname: Chen – volume: 282 start-page: 429 year: 2005 end-page: 451 ident: b10 article-title: Scattering of plate waves by a cylindrical inhomogeneity publication-title: J. Sound Vib. contributor: fullname: Chang – volume: 116 start-page: 154 issue: 1 year: 2004 ident: 10.1016/j.wavemoti.2017.08.006_b1 article-title: Mindlin plate theory for damage detection: Source solutions publication-title: J. Acoust. Soc. Am. doi: 10.1121/1.1739482 contributor: fullname: Rose – volume: 2 start-page: 2004 year: 1964 ident: 10.1016/j.wavemoti.2017.08.006_b2 article-title: Diffraction of flexural waves by a cavity in an elastic plate publication-title: J. AIAA doi: 10.2514/3.2716 contributor: fullname: Pao – volume: 146 start-page: 332 year: 2001 ident: 10.1016/j.wavemoti.2017.08.006_b11 article-title: A multiple-scattering scheme for modelling surface wave propagation in isotropic and anisotropic three-dimensional structures publication-title: Geophys. J. Int. doi: 10.1046/j.1365-246x.2001.01460.x contributor: fullname: Maupin – year: 1972 ident: 10.1016/j.wavemoti.2017.08.006_b14 contributor: fullname: Abramowitz – volume: 45 start-page: 162 year: 2008 ident: 10.1016/j.wavemoti.2017.08.006_b5 article-title: Analytical prediction and experimental measurement for mode conversion and scattering of plate waves at non-symmetric circular blind holes in isotropic plates publication-title: Wave Motion doi: 10.1016/j.wavemoti.2007.05.005 contributor: fullname: Cegla – volume: 26 start-page: 1 year: 1997 ident: 10.1016/j.wavemoti.2017.08.006_b4 article-title: Flexural wave propagation and scattering on thin plates using Mindlin theory publication-title: Wave Motion doi: 10.1016/S0165-2125(97)00016-4 contributor: fullname: Vemula – volume: 127 start-page: 754 issue: 2 year: 2010 ident: 10.1016/j.wavemoti.2017.08.006_b7 article-title: Mindlin plate theory for damage detection: Imaging of flexural inhomogeneities publication-title: J. Acoust. Soc. Am. doi: 10.1121/1.3277217 contributor: fullname: Rose – volume: 40 start-page: 309 year: 1975 ident: 10.1016/j.wavemoti.2017.08.006_b13 article-title: Three-dimensional induced polarization and electromagnetic modeling publication-title: Geophysics doi: 10.1190/1.1440527 contributor: fullname: Hohmann – volume: 181 start-page: 115 year: 1995 ident: 10.1016/j.wavemoti.2017.08.006_b3 article-title: Scattering of flexural waves on thin plates publication-title: J. Sound Vib. doi: 10.1006/jsvi.1995.0129 contributor: fullname: Norris – volume: 282 start-page: 429 year: 2005 ident: 10.1016/j.wavemoti.2017.08.006_b10 article-title: Scattering of plate waves by a cylindrical inhomogeneity publication-title: J. Sound Vib. doi: 10.1016/j.jsv.2004.02.023 contributor: fullname: Wang – volume: 129 start-page: 1280 issue: 3 year: 2011 ident: 10.1016/j.wavemoti.2017.08.006_b16 article-title: Influence of stacking sequence on scattering characteristics of the fundamental anti-symmetric lamb wave at through holes in composite laminates publication-title: J. Acoust. Soc. Am. doi: 10.1121/1.3533742 contributor: fullname: Veidt – volume: 129 start-page: 1288 issue: 3 year: 2011 ident: 10.1016/j.wavemoti.2017.08.006_b8 article-title: Scattering of the fundamental anti-symmetric Lamb wave at delaminations in composite laminates publication-title: J. Acoust. Soc. Am. doi: 10.1121/1.3533741 contributor: fullname: Ng – volume: 329 start-page: 1042 year: 2010 ident: 10.1016/j.wavemoti.2017.08.006_b6 article-title: Scattering of flexural wave in a thin plate with multiple circular inclusions by using the null-field integral equation approach publication-title: J. Sound Vib. doi: 10.1016/j.jsv.2009.10.017 contributor: fullname: Lee – volume: 331 start-page: 4870 year: 2012 ident: 10.1016/j.wavemoti.2017.08.006_b9 article-title: Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates publication-title: J. Sound Vib. doi: 10.1016/j.jsv.2012.06.002 contributor: fullname: Ng – year: 2007 ident: 10.1016/j.wavemoti.2017.08.006_b15 contributor: fullname: Gradshteyn – volume: 174 start-page: 857 year: 2008 ident: 10.1016/j.wavemoti.2017.08.006_b12 article-title: Scattering of surface waves modelled by the integral equation method publication-title: Geophys. J. Int. doi: 10.1111/j.1365-246X.2008.03787.x contributor: fullname: Lu |
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| Snippet | The characteristics of defects in plate-like structures can be extracted from the scattered flexural waves. The scattering of flexural waves is studied in this... |
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| SubjectTerms | Approximation Born approximation Exponential functions Flexural wave Hankel functions Inhomogeneity Integral equations Integration Mathematical analysis Mindlin plate Mindlin plates Near-field effect Plate theory Plates (structural members) Scattering Scattering amplitude Singular integration Sound waves |
| Title | Scattering of flexural waves by an inhomogeneity in a thin plate |
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