ВОЛНОВЫЕ ПРОЦЕССЫ В ТРЕХСЛОЙНЫХ ОБОЛОЧКАХ ВРАЩЕНИЯ С УЧЕТОМ ДИСКРЕТНОСТИ ЗАПОЛНИТЕЛЯ ПРИ НЕСТАЦИОНАРНЫХ НАГРУЗКАХ

Abstract

Thin-walled shell structures in the form of plates and shells of various shapes have a high bearing capacity, lightness, and relative ease of manufacture. Three-layer shell elements, which consist of two bearing layers and a filler, which ensures their joint work, are widely used in mechanical engineering, industrial and civil construction, aviation and space technology, shipbuilding. When calculating the strength of three-layer shell structures with a discrete filler under dynamic loads, it becomes necessary to determine the stress-strain state both in the area of a sharp change in the geometry of the structure and at a considerable distance from the heterogeneity. The complexity of the processes that arise in this case necessitates the use of modern numerical methods for solving dynamic problems of the behavior of three-layer shell elements with a discrete filler. In this regard, the determination of the stress-strain state of three-layer shells with a discrete filler under non-stationary loads and the development of an effective numerical method for solving problems of this class is an urgent problem in the mechanics of a deformable solid. On the basis of the theory of threelayered shells with applying the hypotheses for each layer the nonstationary vibrations threelayered shells of revolution with allowance of discrete fillers are investigated. Hamilton-Ostrogradskyy variational principle for dynamical processes is used for deduction of the motion equations. An efficient numerical method for solution of problems on nonstationary behaviour of threelayers shells of revolution with allowance of discrete fillers are used. The wide diapason of geometrical, and physico-mechanical parameters of nonhomohenes threelayered structure are considerated. On the basis of the offered model nonstationary problems of the forced nonlinear vibrations of threelayered shells of revolution of various structure are solved and analysed. The basis of the developed numerical method for the study of nonstationary oscillations is the application of explicit finite-difference schemes to solve the initial differential equations in partial derivatives. The theory is based on the relations of the theory of three-layer shells of revolution taking into account the discreteness of the filler, which are based on the hypotheses of the geometrically nonlinear theory of shells and rods of the Timoshenko type.