The inverse transient problem of identifying the law of change in the cross-sectional area of an elastic bar

Abstract

The main goal of investigations is to obtain solutions for new inverse transient problems of elastic bars. The research objective is to develop and realize new methods, approaches and algorithms for solving inverse transient problems of bar mechanics. The direct transient task for elastic bar consists in determining elastic displacements, which satisfies a given equation of transient oscillations in partial derivatives and some given initial and boundary conditions. The solution of inverse problem with a completely unknown space-time law of load distribution is based on the method of influence functions. With its application the inverse 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 bar. To solve it, the method of mechanical quadratures is used in combination with the Tikhonov regularization method.