An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods
Elastic wave propagation in weakly nonlinear elastic rods is considered in the time domain. The method of wave splitting is employed to formulate a standard scattering problem, forming the mathematical basis for both direct and inverse problems. A quasi-linear version of the Wendroff scheme (FDTD) i...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X0210903X |
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| _version_ | 1849306131638255616 |
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| author | Shinuk Kim Kevin L. Kreider |
| author_facet | Shinuk Kim Kevin L. Kreider |
| author_sort | Shinuk Kim |
| collection | DOAJ |
| description | Elastic wave propagation in weakly nonlinear elastic rods is considered in the time domain. The method of wave splitting is employed to formulate a standard scattering problem, forming the mathematical basis for both direct and inverse problems. A quasi-linear version of the Wendroff scheme (FDTD) is used to solve the direct problem. To solve the inverse problem, an asymptotic expansion is used for the wave field; this linearizes the order equations, allowing the use of standard numerical techniques. Analysis and numerical results are presented for three model inverse problems: (i) recovery of the nonlinear parameter in the stress-strain relation for a homogeneous elastic rod, (ii) recovery of the cross-sectional area for a homogeneous elastic rod, (iii) recovery of the elastic modulus for an inhomogeneous elastic rod. |
| format | Article |
| id | doaj-art-3984b35d64c24ce0a22efecebeeeb7f0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3984b35d64c24ce0a22efecebeeeb7f02025-08-20T03:55:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422002-01-012840743510.1155/S1110757X0210903XAn asymptotic approach to inverse scattering problems on weakly nonlinear elastic rodsShinuk Kim0Kevin L. Kreider1Department of Theoretical and AppliedMathematics, The University of Akron, Akron 44325-4002, OH, USADepartment of Theoretical and AppliedMathematics, The University of Akron, Akron 44325-4002, OH, USAElastic wave propagation in weakly nonlinear elastic rods is considered in the time domain. The method of wave splitting is employed to formulate a standard scattering problem, forming the mathematical basis for both direct and inverse problems. A quasi-linear version of the Wendroff scheme (FDTD) is used to solve the direct problem. To solve the inverse problem, an asymptotic expansion is used for the wave field; this linearizes the order equations, allowing the use of standard numerical techniques. Analysis and numerical results are presented for three model inverse problems: (i) recovery of the nonlinear parameter in the stress-strain relation for a homogeneous elastic rod, (ii) recovery of the cross-sectional area for a homogeneous elastic rod, (iii) recovery of the elastic modulus for an inhomogeneous elastic rod.http://dx.doi.org/10.1155/S1110757X0210903X |
| spellingShingle | Shinuk Kim Kevin L. Kreider An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods Journal of Applied Mathematics |
| title | An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods |
| title_full | An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods |
| title_fullStr | An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods |
| title_full_unstemmed | An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods |
| title_short | An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods |
| title_sort | asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods |
| url | http://dx.doi.org/10.1155/S1110757X0210903X |
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