Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2, Number 8 (2002), 407-435.
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) 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.
J. Appl. Math., Volume 2, Number 8 (2002), 407-435.
First available in Project Euclid: 30 March 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 74J30: Nonlinear waves 74B20: Nonlinear elasticity
Secondary: 74H10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) 74J25: Inverse problems 65M32: Inverse problems 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
Kim, Shinuk; Kreider, Kevin L. An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods. J. Appl. Math. 2 (2002), no. 8, 407--435. doi:10.1155/S1110757X0210903X. https://projecteuclid.org/euclid.jam/1049074736