April  2016, 9(2): 427-444. doi: 10.3934/dcdss.2016005

Few remarks on the use of Love waves in non destructive testing

1. 

Département d'ingénierie mathématique, Conservatoire National des Arts et Métiers, 292, rue saint Martin, 75003 Paris, France

2. 

Laboratoire de mathématiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France

Received  January 2015 Revised  October 2015 Published  March 2016

This paper concerns a theoretical study on the possibility of using Love waves for non destructive testing. A mathematical model is presented and analyzed. Several numerical tests are given in order to show the mechanical behaviour of this model.
Citation: Philippe Destuynder, Caroline Fabre. Few remarks on the use of Love waves in non destructive testing. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 427-444. doi: 10.3934/dcdss.2016005
References:
[1]

M. Amara, Ph. Destuynder and M. Djaoua, On a finite element schem for plane crack problems,, Numer. Meth. in Frac. Mech., (1980), 41.   Google Scholar

[2]

H. Brezis, Analyse Fonctionnelle,, Masson, (1983).   Google Scholar

[3]

H. D. Bui, Mécanique de la Rupture Fragile,, Masson, (1979).   Google Scholar

[4]

P. G. Ciarlet, The Finite Element Mehod for Elliptic Problems,, Elsevier, (1978).   Google Scholar

[5]

Ph. Destuynder and C. Fabre, Singularities occuring in multimaterials with traPHDCF3nsparent boundary conditions,, to appear in Quaterly of Applied Maths, (2016).   Google Scholar

[6]

Ph. Destuynder and C. Fabre, On the Detection of Cracks in Linear Elasticity,, research report CNAM, (2015).   Google Scholar

[7]

Ph. Destuynder and M. Djaoua, Sur une interpretation mathématique de l'intégrale de Rice en mécanique de la rupture fragile,, Mathematical Methods in the Applied Sciences, 3 (1981), 70.  doi: 10.1002/mma.1670030106.  Google Scholar

[8]

G. Diot, A. Kouadri-David, L. Dubourg, J. Flifla, S. Guegan and E. Ragneau, Mesures de Défauts par Ultrasons Laser Dans Des Soudures D'alliage D'aluminium,, Publications du CETIM, (2014).   Google Scholar

[9]

M. Dobrowolski, Numerical Approximation of Elliptic Interface and Corner Problems,, Habilitationsschrift, (1981).   Google Scholar

[10]

J.-C. Dumont-Fillon, Contrôle non Destructif Par Les Ondes de Love et Lamb,, Editions Techniques de l'ingénieur, (2012).   Google Scholar

[11]

A. Galvagni and P. Cawley, The reflection of guided waves from simple supports in pipes,, AIP Conf. Proc., 105 (2011).  doi: 10.1063/1.3591845.  Google Scholar

[12]

E. Holmgren, Über systeme von linearen partiellen differentialgleichungen, Öfversigt af kongl,, Vetenskaps-Academien Förhandlinger, 58 (1901), 91.   Google Scholar

[13]

M. J. S. Lowe, Characteristics of the reflection of Lamb waves from defects in plates and pipes,, Review of Progress in Quantitative NDE, 17 (2002), 113.  doi: 10.1007/978-1-4615-5339-7_14.  Google Scholar

[14]

S. G. Mallat, A Wavelet Tour of Signal Processing,, Academic Press, (1999).   Google Scholar

[15]

P. M. Marty, Modelling of Ultrasonic Guided Wave Field Generated by Piezoelectric Transducers,, Thesis at Imperial college of science, (2002).   Google Scholar

[16]

J. Necas, Les Méthodes Directes en Théorie des Équations Elliptiques,, Masson, (1965).   Google Scholar

[17]

P. A. Raviart and J. M. Thomas, Approximation des Équations aux Dérivées Partielles,, Masson, (1986).   Google Scholar

[18]

R. Ribichini, F. Cegla, P. Nagy and P. Cawley, Study and comparison of different EMAT configurations for SH wave inspection,, IEEE Trans.UFFC, 58 (2011), 2571.  doi: 10.1109/TUFFC.2011.2120.  Google Scholar

[19]

G. Strang and G. Fix, Analysis of the Finite Elements Method,, Prentice Hall; Edition: First Edition, (1973).   Google Scholar

[20]

A. N. Tychonoff, Solution of incorrectly formulated problems and the regularization method,, Soviet Math Dokl, 4 (2011), 1035.   Google Scholar

[21]

D. Zagier, The Dilog function,, , (2007).   Google Scholar

show all references

References:
[1]

M. Amara, Ph. Destuynder and M. Djaoua, On a finite element schem for plane crack problems,, Numer. Meth. in Frac. Mech., (1980), 41.   Google Scholar

[2]

H. Brezis, Analyse Fonctionnelle,, Masson, (1983).   Google Scholar

[3]

H. D. Bui, Mécanique de la Rupture Fragile,, Masson, (1979).   Google Scholar

[4]

P. G. Ciarlet, The Finite Element Mehod for Elliptic Problems,, Elsevier, (1978).   Google Scholar

[5]

Ph. Destuynder and C. Fabre, Singularities occuring in multimaterials with traPHDCF3nsparent boundary conditions,, to appear in Quaterly of Applied Maths, (2016).   Google Scholar

[6]

Ph. Destuynder and C. Fabre, On the Detection of Cracks in Linear Elasticity,, research report CNAM, (2015).   Google Scholar

[7]

Ph. Destuynder and M. Djaoua, Sur une interpretation mathématique de l'intégrale de Rice en mécanique de la rupture fragile,, Mathematical Methods in the Applied Sciences, 3 (1981), 70.  doi: 10.1002/mma.1670030106.  Google Scholar

[8]

G. Diot, A. Kouadri-David, L. Dubourg, J. Flifla, S. Guegan and E. Ragneau, Mesures de Défauts par Ultrasons Laser Dans Des Soudures D'alliage D'aluminium,, Publications du CETIM, (2014).   Google Scholar

[9]

M. Dobrowolski, Numerical Approximation of Elliptic Interface and Corner Problems,, Habilitationsschrift, (1981).   Google Scholar

[10]

J.-C. Dumont-Fillon, Contrôle non Destructif Par Les Ondes de Love et Lamb,, Editions Techniques de l'ingénieur, (2012).   Google Scholar

[11]

A. Galvagni and P. Cawley, The reflection of guided waves from simple supports in pipes,, AIP Conf. Proc., 105 (2011).  doi: 10.1063/1.3591845.  Google Scholar

[12]

E. Holmgren, Über systeme von linearen partiellen differentialgleichungen, Öfversigt af kongl,, Vetenskaps-Academien Förhandlinger, 58 (1901), 91.   Google Scholar

[13]

M. J. S. Lowe, Characteristics of the reflection of Lamb waves from defects in plates and pipes,, Review of Progress in Quantitative NDE, 17 (2002), 113.  doi: 10.1007/978-1-4615-5339-7_14.  Google Scholar

[14]

S. G. Mallat, A Wavelet Tour of Signal Processing,, Academic Press, (1999).   Google Scholar

[15]

P. M. Marty, Modelling of Ultrasonic Guided Wave Field Generated by Piezoelectric Transducers,, Thesis at Imperial college of science, (2002).   Google Scholar

[16]

J. Necas, Les Méthodes Directes en Théorie des Équations Elliptiques,, Masson, (1965).   Google Scholar

[17]

P. A. Raviart and J. M. Thomas, Approximation des Équations aux Dérivées Partielles,, Masson, (1986).   Google Scholar

[18]

R. Ribichini, F. Cegla, P. Nagy and P. Cawley, Study and comparison of different EMAT configurations for SH wave inspection,, IEEE Trans.UFFC, 58 (2011), 2571.  doi: 10.1109/TUFFC.2011.2120.  Google Scholar

[19]

G. Strang and G. Fix, Analysis of the Finite Elements Method,, Prentice Hall; Edition: First Edition, (1973).   Google Scholar

[20]

A. N. Tychonoff, Solution of incorrectly formulated problems and the regularization method,, Soviet Math Dokl, 4 (2011), 1035.   Google Scholar

[21]

D. Zagier, The Dilog function,, , (2007).   Google Scholar

[1]

Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533

[2]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825

[3]

Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209

[4]

Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017

[5]

Samir Adly, Oanh Chau, Mohamed Rochdi. Solvability of a class of thermal dynamical contact problems with subdifferential conditions. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 91-104. doi: 10.3934/naco.2012.2.91

[6]

M. Mahalingam, Parag Ravindran, U. Saravanan, K. R. Rajagopal. Two boundary value problems involving an inhomogeneous viscoelastic solid. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1351-1373. doi: 10.3934/dcdss.2017072

[7]

Masahiro Ikeda, Ziheng Tu, Kyouhei Wakasa. Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021011

[8]

Lingyu Li, Zhang Chen. Asymptotic behavior of non-autonomous random Ginzburg-Landau equation driven by colored noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3303-3333. doi: 10.3934/dcdsb.2020233

[9]

Haili Qiao, Aijie Cheng. A fast high order method for time fractional diffusion equation with non-smooth data. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021073

[10]

Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021

[11]

Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271

[12]

Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044

[13]

Valery Y. Glizer. Novel Conditions of Euclidean space controllability for singularly perturbed systems with input delay. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 307-320. doi: 10.3934/naco.2020027

[14]

Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817

[15]

Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189

[16]

Habib Ammari, Josselin Garnier, Vincent Jugnon. Detection, reconstruction, and characterization algorithms from noisy data in multistatic wave imaging. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 389-417. doi: 10.3934/dcdss.2015.8.389

[17]

Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329

[18]

Feng Luo. A combinatorial curvature flow for compact 3-manifolds with boundary. Electronic Research Announcements, 2005, 11: 12-20.

[19]

Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223

[20]

Marco Ghimenti, Anna Maria Micheletti. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1757-1778. doi: 10.3934/dcdss.2020453

2019 Impact Factor: 1.233

Metrics

  • PDF downloads (47)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]