A general formulation of the prestress field reconstruction problem in the analysis of the stationary vibration is represented. The direct problem solving methods of determining the displacement vector components for one-dimensional (Fredholm integral equations of the second kind) and two-dimensional (FEM) areas are proposed. The practical recommendations of the uniaxial prestress state identification are given. The iterative process based on solving the Fredholm integral equation of the first kind using Tikhonov's regularization procedure is described for solving the inverse problem. Numerical experiments on the reconstruction of monotonic and nonmonotonic unknown function are briefly characterized.
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