Inverse scattering problem for detecting a defect in a magnetoelastic layer

References

• Knopoff L. The interaction between elastic wave motions and a magnetic field in electrical conductors. J Geophys Res Solid Earth. 1995;60(4):441–456.
   Google Scholar
• Dunkin J, Eringen A. On the propagation of waves in an electromagnetic elastic solid. In J Eng Sci. 1963;1:461–495.
   Google Scholar
• Maugin G. Wave motion in magnetizable deformable solids. Int J Eng Sci. 1981;19:321–388.
   Google Scholar
• Das N, Bhattacharya S. Axisymmetric vibrations of orthotropic shells in a magnetic field. J Pure Appl Math. 1978;45(1):40–54.
   Google Scholar
• Gourakishwar O. Propagation of waves in magnetoelastic media. J Appl Phys. 1990;67(2):725–733.
   Google Scholar
• Andreou E, Dassios G. Dissipation of energy for magnetoelastic waves in conductive medium. Quarterly Appl Math. 1997;55:23–39.
   Google Scholar
• Kaliski S. Cerenkov generation of thermal waves for the wave equations of Thermo-Electro-Magneto-Elasticity. Proceedings of Symposium on Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids; Vienna: Springer; 1968.
   Google Scholar
• Eringen A, Maugin G. Electrodynamics of continua I. foundations and solid media. 2nd ed. New York: Springer; 1990. 47–90.
   Google Scholar
• Parton V, Kudryavtsev B. Electromagnetoelasticity, Piezoelectrics and electricity conducting solids. New York: Gordon and Breach Science Publisher; 1988. 10–100.
   Google Scholar
• Lee JS, Its EN. Propagation of Rayleigh waves in magneto-elastic media. J Appl Mech. 1992;59(4):812–818.
   Google Scholar
• Acharya DP, Maji C. Effect of surface stress on magneto-elastic surface waves in finitely conducting media. Acta Geophys. 2007;55(4):554–576.
   Google Scholar
• Narain S. Magneto-elastic Rayleigh waves on the surface of orthotropic cylinder of varying density. Defence Sci J. 1985;35(4):435–442.
   Google Scholar
• Acharya DP, Roy I. Magnetoelastic surface waves in electrically conducting fibre-reinforced media. Bullet Inst Math Academia Sinica (New Series). 2009;4(3):333–352.
   Google Scholar
• Lin CB, Lin HM. The magnetoelastic problem of cracks in bonded dissimilar materials. Int J Solids Struct. 2002;39:2807–2826.
   Google Scholar
• Rogowski B. Analysis of a penny-shaped crack in magneto-elastic medium. J Theoretical Appl Mech. 2009;47(1):143–159.
   Google Scholar
• Bagdasarian GY, Hasanian DJ. Magnetoelastic interaction between a soft ferromagnetic elastic half-plane with a crack and a constant magnetic field. Int J Solids Struct. 2002;37(38):5371–5383.
   Google Scholar
• Zhao SX, Lee KY. Interfacial crack problem in layered soft ferromagnetic materials in uniform magnetic field. Mech Res Commun. 2007;34(1):19–30.
   Google Scholar
• Wei L, Yapeng S, Daining F. Magnetoelastic coupling on soft ferromagnetic solids with an interface crack. Acta Mech. 2002;154(1-4):1–9.
   Google Scholar
• Hasebe N, Wang XF, Nakanishi H. On magnetoelastic problems of a plane with an arbitrarily shaped hole under stress and displacement boundary conditions. Quarterly J Mech Appl Math. 2007;60(4):423–442.
   Google Scholar
• Nowacki W. Two-dimensional problem of magnetothermoelasticity I. Bulletin De Academit Polonaise Des Science-Serie Des Science Techniques. 1965;13(5):485–493.
   Google Scholar
• Sladek V, Sladek J. Boundary integral method in magnetoelasticity. Int J Eng Sci. 1988;26(5):401–418.
   Google Scholar
• Fang X, Hua C, Huang W. Dynamic stress of a circular cavity buried in a semi-infinite functionally graded piezoelectric material subjected to shear waves. Europian J Mech-A/Solids. 2007;26:1016–1028.
   Google Scholar
• Fang X. Multiple scattering of electro-elastic waves from a buried cavity in a functionally graded piezoelectric material layer. Int J Solids Struct. 2008;45:5716–5729.
   Google Scholar
• Jinxi L, Xianglin L, Yongbin Z. Green's functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. Int J Eng Sci. 2001;39:1405–1418.
   Google Scholar
• Qin Q. 2D Green's functions of defective magnetoelectroelastic solids under thermal loading. Eng Anal Boundary Elements. 2005;29:577–585.
   Google Scholar
• Lorenzi A, Priimenko V. Identification problem related to electro -magneto-elastic interactions. J Inverse Ill-posed Prob. 1996;4:115–143.
   Google Scholar
• Priimenko V, Vishnevskii M. An inverse problem of electromagnetoelasticity in the case of complete nonlinear interaction. J Inverse Ill-posed Prob. 2005;13(3):277–301.
   Google Scholar
• Priimenko V, Vishnevskii M. Mathematical problems of electromagnetoelastic interactions. Boletim Da Sociedade Paranaense De Matematica. 2007;25:55–66.
   Google Scholar
• Avdeev A, Soboleva O, Priimenko V. Inverse problem of Electro-magnetoelasticity: simultaneous determination of elastic and electromagnetic parameters. Proceedings of Symposium on Applied and Industrial Mathematics; Italy: Springer; 1998.
   Google Scholar
• Romanov V. A stability of the solution to a two-dimensional inverse problem of electrodynamics. Siberian Math J. 2003;44:659–670.
   Google Scholar
• Lu Y, Ye L, Su Z, et al. Artificial neural network (ANN)-based crack identification in aluminum plates with lamb wave signals. J Intelligent Mater Syst Struct. 2009;20(1):39–49.
   Google Scholar
• Hattori G, Saez A. Damage identification in multifield materials using neural networks. Inverse Prob Sci Eng. 2013;21(6):929–944.
   Google Scholar
• Sumbatyan M, Elmorabie KM, Brigante M. Detection of a buried void void in an elastic layer of constant thickness: the anti-plane problem: anti-Plane problem. Math Mech Solids. 2012;18(1):67–77.
   Google Scholar
• Elmorabie KM, Sumbatyan M. Detection of a single elliptic-shape buried Object in stratified elastic media: anti-Plane problem. Europian J Mech-A/Solids. 2013;37:1–7.
   Google Scholar
• Elmorabie KM, Sumbatyan M. Inverse diffraction problems for buried objects in the layered elastic media: the anti-plane problem. Inverse Prob Sci Eng. 2018;26(11):1540–1560.
   Google Scholar
• Elmorabie KM, Yahya R. The scattering waves from an object in an elastic-fluid layered structure. ZAMM-J Appl Math Mech/Zeitschrift Fur Angewandte Mathematik Und Mechanik. 2019;99(5):1–15.
   Google Scholar
• Achenbach J. Reciprocity in elastodynamics. UK: Cambridge University Press; 2003.
   Google Scholar
• Chattopadhyay A, Maugin GA. Diffraction of magnetoelastic shear waves by a rigid strip. J Acoust Soc Am. 1985;78(1):217–222.
   Google Scholar
• Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. New York: Springer-Verlag; 2013. 46–51.
   Google Scholar
• Abo-el-nour NA, Alshaikh NF. The dispersion relation of flexural waves in a magnetoelastic anisotropic circular cylinder. Adv in Phys Theor Appl. 2013;13:20–33.
   Google Scholar
• Brebbia CA, Dominguez J. Boundary elements: an introductory course. 2nd ed. New York: WIT press; 1994. 50–57.
   Google Scholar
• Jiles DC, Chang TT, Hougen DR, et al. Stress-induced changes in the magnetic properties of some nickel-copper and nickel-cobalt alloys. J Appl Phys. 1988;64(7):3620–3628.
   Google Scholar
• Aaaaa CCC. Conductivity and resistivity values for copper and alloys. 2019. Available From: https://www.nde-ed.org/GeneralResources/MaterialProperties/ET/ConductivityCopper[On-line].
   Google Scholar
• Borovikov V, Fradkin L. Scatter of a plane elastic wave by a rough crack edge. Russian J Math Phys. 2009;16(2):166–187.
   Google Scholar
• Sumbatyan MA, Scalia A. Equations of mathematical diffraction theory. Florida: CRC Press; 2005.275–325.
   Google Scholar
• Priimenko V, Vishnevskii M. An evolution problem related to nonlinear 2d-magnetoelasticity. Appl Math Lett. 2018;76:28–33.
   Google Scholar
• Fletcher R. Practical methods of optimization. 2nd ed. New York: John Wiley & Sons; 2000. 49–56.
   Google Scholar
• Ramesh PS, Lean MH. Accurate integration of singular kernels in boundary integral formulations for Helmholtz equation. Int J Numer Methods Eng. 1991;31(6):1055–1068.
   Google Scholar