An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods. Issue 8 (3rd December 2002)

• Record Type: Journal Article
• Authors: Kim, Shinuk; Kreider, Kevin L.
• Is Part Of: Journal of applied mathematics. Volume 2:Issue 8(2002)
• Page Start: 407
• Page End: 435
• Publication Date: 2002-12-03
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/S1110757X0210903X
• Languages: English
• ISSNs: 1110-757X

Abstract

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.