On the reconstruction of material properties of a radially inhomogeneous cylindrical waveguide

Abstract

The scheme of solving the inverse problem (IP) for reconstructing three functions characterizing the radial change in the Lamé parameters and in the density in a cylindrical waveguide is presented. The displacement fields corresponding to three types of loading are used as an additional information for solving the IP. An iterative process is constructed, at each step of which a direct problem is solved for the radially inhomogeneous waveguide, and the corrections to the restored functions are determined. The corrections are identified by solving the system of three Fredholm integral equations of the first kind with smooth kernels. The solution is constructed by the A. N. Tikhonov regularization method. A series of computational experiments was carried out. The role of the initial approximation and the frequency range is discussed.