ІДЕНТИФІКАЦІЯ МОМЕНТІВ ТЕРТЯ В ШАРНІРНИХ ОПОРАХ БАЛКИ ТИМОШЕНКА ПРИ НЕСТАЦІОНАРНОМУ НАВАНТАЖЕННІ

Structural elements with hinged support are widely used both in engineering and in plants to study the deformation of various structural elements. Consideration of friction in hinged supports is necessary for modeling natural conditions. It is also possible to use friction in joints to damp vibrations. The purpose of this work is to develop a method of identification of friction moments in the hinge supports of Timoshenko beam under its non-stationary loading. The loading scheme of the beam under symmetric arrangement of supports relative to the point of application of non-stationary concentrated force was considered. Identification was carried out on the deflection of a certain point of the beam as a function of time. The system of differential equations for the Timoshenko beam was used to model the beam vibrations. The solution of this system was obtained using Fourier series expansion of unknown functions and Laplace transform. The Tikhonov regularization method was used to solve the inverse problem for identification of friction moments in hinge supports. As a result of the study, a method for identification of friction moments in hinged supports for Timoshenko beam was developed. A numerical experiment was carried out. The deflection at some point of the beam (as a function of time), which was obtained by solving the direct problem, was taken as input data. The influence of inaccuracy of initial data setting on stability and identification accuracy was investigated. The results of calculations have shown that the developed method of identification based on the use of the Tikhonov regularization method allows to effectively obtain a stable solution of the corresponding inverse problem even without preliminary processing of the initial data. The developed method of identification of friction moments in hinge supports can be further developed for more complex loading schemes of beams, as well as for other types of structural elements.