Yegorov P. The integral Volterra equations in non-stationary problems for elastic structural elements

The object of research is non-stationary deforming of elastic structural elements caused by external impulse loads. The aim of research is development of methods for identifying impulse loads acting on the structural elements as membranes, rods, beams, plates and cylindrical shells, as well as methods for solving inverse non-stationary problems in determining the parameters of mechanical systems. Research methods - the theory of Volterra integral equations, the Laplace integral transforms, the theory of Fourier series, the theory of generalized functions, the regularization method, analytic-numerical methods of mathematical physics, the finite difference method, the finite element method, the d'Alembert method. The theoretical value of the developed methods lies in supplement the existing models of mechanical systems by taking into account the influence of the attached objects, which makes it possible to make more accurate models of existing and prospective constructions and technical systems, as well as in the development of stable to perturbations of the initial data methods for recovering non-stationary loads acting on considered mechanical systems. The novelty of the results is the creation of methods for studying the stress-strain state of structural elements, methods for identifying non-stationary loads and unknown parameters of mechanical systems, which, unlike previous methods, allow to take into account the influence of the attached objects. Is proposed the technique for simultaneous identification of the application point and the time dependence of the disturbing load. The implementation of the research results was carried out at the Kharkiv National Automobile and Highway University and in RPE "Khartron-Plant". The field of application - mechanical engineering, oil and gas industry.