НЕСТАЦІОНАРНА РЕАКЦІЯ ЦИЛІНДРИЧНОЇ ОБОЛОНКИ З ПРУЖНИМ ШАРОМ НА ДІЮ РУХОМОГО РАДІАЛЬНОГО НАВАНТАЖЕННЯ

Abstract

An analysis of studies and publications on the issues of determining the stress-strain state of constituent structures has shown that the problems of choosing and modeling the operation of structures in the form of infinitely long cylindrical shells with a soft, weightless elastic layer have not received enough attention in the scientific literature today. The use of modern approaches to the construction of mathematical models and algorithms makes it possible to take into account various kinds of dynamic loads that are transferred to structural elements in the form of cylindrical shells.The aim of the article is to develop an analytical method for calculating cylindrical shells with a weightless soft elastic layer under the action of a moving radial load.Based on the principles and approaches to the analysis of non-stationary dynamic processes in complex shells, the paper presents an algorithm based on the application of the integral Fourier transform along the axial coordinate, as well as the use of the Runge-Kutta numerical method for integrating the transformed differential equations of shell motion in the image space. Cases of load movement with different speeds and uniform pressure wave movement are considered. The dependence of the radial displacements of the shell on the reaction of the elastic layer, represented by an approximate model, taking into account only the radial displacement, is determined. The cases of motion of a radial axisymmetric load both with constant and with varying speed are investigated. The distribution of shell deflections along the length is given for different moments of time during the movement of the load at a constant speed, as well as for the slow movement of the ring load.In this work, for the first time, a mathematical model of the non-stationary behavior of a shell with an outer layer under the action of a moving load is constructed. A comparative analysis of various shell models has been carried out and deformation patterns of both accelerated and slow motion have been constructed. The transient processes that occur at the moment of load application and the subsequent time intervals immediately after this moment are considered. The presented materials can be used for dynamic modeling of the operation of structures in the form of plates and shells.