Identification of the inhomogeneous cylindrical waveguide properties

The inverse coefficient problem of properties identification for the radially inhomogeneous (including layered and coated) elastic cylindrical isotropic waveguide is studied. To restore three functions - the Lame and density coefficients characterizing the variable properties of an isotropic waveguide, two modes of action on an object that excite normal and torsional oscillations are considered. The identification procedure is carried out according to the acoustic sounding of the outer surface of the cylinder. The problem by the integral Fourier transformation at the coordinate coinciding with the axis of the waveguide is reduced to one-dimensional problems concerning the averaged characteristics. The obtained problems are divided by the unknown functions which allow to realize the serial identification. The linearization of the divided inverse coefficient problems is carried out. Two iterative processes are formulated, which allow to restore the required functions sequentially. At each step of the iterative schemes, the corresponding boundary value problems are solved by the method of adjustment and the system of Fredholm's integral equations of the first kind with smooth kernels by using of regularization methods. A computational experiment simulating normal and torsional oscillations of the waveguide is conducted. The corresponding wave fields obtained from the solution of the direct problem by the known laws of inhomogeneity are used as additional information. We study examples of identifying the laws of waveguide characteristics change which model the presence of inhomogeneous coating on the outer surface, which characteristics can significantly differ from those of the waveguide material, which are considered in these experiments to be known. We perform a representative set of computational experiments to identify the laws of changing the required mechanical characteristics - the modules of elasticity and density - for monotonic, non-monotonic and piecewise continuous functions.