Abstract
The problem of determining the characteristics of the sensitivity of inhomogeneous isotropic elastic solids with respect to three functions characterizing the inhomogeneity - Lame coefficients and density - is considered. The corresponding boundary value problems are formulated, equations for determining the sensitivity are obtained. An example is presented for a cylindrical rod in the analysis of longitudinal and bending oscillations, the sensitivity to changes in Young's modulus and density is analyzed. Using the iterative algorithm and the A.N. Tikhonov's regularization method, a number of inverse problems were solved to determine these characteristics for monotone and non-monotone laws of their change, and the results of computational experiments are presented. The norm of the difference between the exact and reconstructed solutions is analyzed. Recommendations are given for choosing the most efficient frequency range for sounding from the point of view of reconstruction.
Published Version
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