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On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder

The problem of axisymmetric vibrations of a functionally graded finite hollow cylinder is considered. The ends of the cylinder are thermally insulated and are in a sliding fit. Zero temperature is maintained on the inner surface of the cylinder, free from stress, and a combined thermal and power load acts on the outer surface. The direct problem after applying the Laplace transform is solved based on the method of separation of variables. A set of canonical linear systems of differential equations of the 1st order is obtained, the solution of each of which is obtained numerically using the shooting method. The coefficient inverse problem of finding the thermomechanical characteristics of a finite length cylinder using additional information in Laplace transforms, given on the outer surface of the cylinder, is posed. The dimensionless thermomechanical characteristics of the cylinder were restored in two stages. At the first stage, the initial approximation was determined in the class of positive bounded functions. At the second stage, based on the solution of the corresponding Fredholm integral equations of the 1st kind, corrections of the reconstructed functions were found, and an iterative process of their refinement was constructed. In the course of computational experiments, it was found that monotonic characteristics are restored with good accuracy; the reconstruction procedure is resistant to input information noise.