Investigation of the inverse coefficient problem for a strip

The inverse coefficient problem for an anisotropic inhomogeneous elastic strip is investigated. The mode of steady anti‐plane and plane oscillations is considered. The case of cubic anisotropy is considered. The inverse problem is solved using information about the displacement fields measured in the mode of positional probing of a part of the upper boundary of the strip. A scheme for reconstructing three functions characterizing the change in the mechanical properties of the strip across the thickness is proposed. The boundary value problem is linearized with respect to the initial state and corrections to it, a solution to the direct problem is obtained using the mathematical apparatus of numerical methods: the shooting method, the Runge–Kutta method, formulas for calculating improper integrals according to the theory of residues. The solution of the inverse coefficient problem for restoring three elastic characteristics is reduced to iterative processes, at each step of which the Fredholm integral equations of the first kind with smooth kernels are solved using the regularization method of A. N. Tikhonov. Computational experiments were performed to restore three unknown laws of change characterizing the inhomogeneous properties of the strip.