The main purpose of the paper is to obtain solutions for new non-stationary inverse problems for elastic rods. The
objective of this study is to develop and implement new methods, approaches and algorithms for solving non-stationary
inverse problems of rod mechanics. The direct non-stationary problem for an elastic rod consists in determining
elastic displacements, which satisfies a given equation of non-stationary oscillations in partial derivatives and some
given initial and boundary conditions. The solution of inverse retrospective problems with a completely unknown
space-time law of load distribution is based on the method of influence functions. With its application, the inverse
retrospective problem is reduced to solving a system of integral equations of the Volterra type of the first kind in time
with respect to the sought external axial load of the elastic rod. To solve it, the method of mechanical quadratures is
used in combination with the Tikhonov regularisation method.

This study was supported by the Russian Science Foundation
(project 20-19-00217).

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