An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods (Q1864540)

Summary: Elastic wave propagation in weakly nonlinear elastic rods is considered in 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 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 a nonlinear parameter in stress-strain relation for a homogeneous elastic rod, (ii) recovery of cross-sectional area for a homogeneous elastic rod, (iii) recovery of elastic modulus for an inhomogeneous elastic rod.