An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods

Shinuk Kim and Kevin L. Kreider

Journal of Applied Mathematics, 2002, vol. 2, 1-29

Abstract:

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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:519743

DOI: 10.1155/S1110757X0210903X

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