Direct and Inverse Problems in Elastic Multilayers with Reflection Data
Source abstract
Abstract
The paper deals with the reflection-transmission process generated by a multilayer with homogeneous, isotropic elastic slabs. The direct problem, namely the determination of reflected and transmitted (and internal) waves in terms of the incident one, is investigated and the solution is proved to exist and be unique. The proof is based on the validity of a first integral. Next the inverse problem is considered to determine the material parameters of the slabs through the measure of the (frequency-dependent) reflection coefficient at the boundary of the multilayer. As a result, the material parameters are found in closed form, though for two slabs only.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in inverse problems · Ultrasonics and Acoustic Wave Propagation · Composite Material Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (17)
Show source-provided references
1. G. Caviglia and A. Morro, Wave reflection and transmission from anisotropic layers through Riccati equations. Q. Jl. Mech. Appl. Math. 55 (2002) 93–107.10.1093/qjmam/55.1.93 ↗
2. R. Burridge, The Gelfand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems. Wave Motion 2 (1980) 305–323.10.1016/0165-2125(80)90011-6 ↗
3. A. Benbelghit, B. Boutassouna, B. Helifa and I.K. Lefkaier, Determination of the elastic properties of some coated materials by simulation of the analogue signal of the reflection acoustic microscope. NDT E Int. 39 (2006) 76–81.10.1016/j.ndteint.2005.06.004 ↗
4. S. He, S. Ström and V.H. Weston, Time Domain Wave-Splittings and Inverse Problems. Oxford University Press (1998) p. 270.
5. E. Ammicht, J.P. Corones and R.J. Krueger, Direct and inverse scattering for viscoelastic media. J. Acoust. Soc. Am. 81 (1987) 827–834.10.1121/1.394561 ↗
6. N.I. Grinberg, Inverse scattering problem for an elastic layered medium. Inverse Problems 7 (1991) 567–576.10.1088/0266-5611/7/4/006 ↗
7. J. Sylvester and D.P. Winebrenner, Linear and nonlinear inverse scattering. SIAM J. Appl. Math. 59 (1998) 669–699.10.1137/S0036139997319773 ↗
8. R.G. Newton, Inversion of reflection data for layered media: A review of exact methods. Geophys. J. R. Astron. Soc. 65 (1981) 191–215.10.1111/j.1365-246X.1981.tb02708.x ↗
9. M. Tadi, Explicit method for inverse wave scattering in solids. Inverse Probl. 13 (1997) 509–521.10.1088/0266-5611/13/2/019 ↗
10. A. Charalambopoulos, On the interior transmission problem in nondissipative, inhomogeneous, anisotropic elasticity. J. Elasticity 67 (2002) 149–170.10.1023/A:1023958030304 ↗
11. L.M. Brekhovskikh, Waves in Layered Media. Academic, New York (1980) p. 7.
12. D.V. Evans, The wide-spacing approximation applied to multiple scattering and sloshing problems. J. Fluid Mech. 210 (1990) 647–658.10.1017/S0022112090001434 ↗
13. D.V. Evans and C.D. Linton, On step approximations for water-wave problems. J. Fluid Mech. 278 (1994) 229–249.10.1017/S002211209400368X ↗
14. G. Caviglia and A. Morro, First integrals and turning points for wave propagation in planarly stratified media. Acta Mech. 169 (2004) 1–11.10.1007/s00707-004-0107-0 ↗
15. P.B. Chapman and J.J. Mahony, Reflection of waves in a slowly varying medium. SIAM J. Appl. Math. 34 (1978) 303–319.10.1137/0134025 ↗
16. V.G. Mozhaev, Some new ideas in the theory of surface acoustic waves in anisotropic media, In: D.F. Parker and A.H. England (eds.), Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics. Kluwer, Dordrecht (1995) pp. 455–462.10.1007/978-94-015-8494-4_63 ↗
17. G. Caviglia and A. Morro, A closed-form solution for reflection and transmission of transient waves in multilayers, J. Acoust. Soc. Am. 116 (2004) 643–654.10.1121/1.1765193 ↗