Istrazivanja i projektovanja za privreduJournal of Applied Engineering Science

THE INVERSE PROBLEM OF RECOVERing AN UNSTEADY LINEAR LOAD FOR AN ELASTIC ROD OF FINITE LENGTH


DOI: 10.5937/jaes0-28073 
This is an open access article distributed under the CC BY 4.0
Creative Commons License

Yana A. Vahterova*
Moscow Aviation Institute (National Research University), Department of Resistance of Materials Dynamics and Strength of Machines, Moscow, Russian Federation

Gregory V. Fedotenkov
Lomonosov Moscow State University, Institute of Mechanics, Moscow, Russian Federation

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.

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

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