In this paper, we consider the natural vibrations of inhomogeneous mechanical systems, i.e., cylindrical bodies located in a deformable viscoelastic medium. The theory and methods for studying the natural vibrations of a cylindrical shell in a viscoelastic medium are constructed. The viscoelastic properties of the medium are taken into account using the hereditary Boltzmann-Walter theory. For the statement of the problem, the general equation of the theory of viscoelasticity in the potentials of displacements in a cylindrical coordinate system is used. An algorithm has been developed to solve the tasks posed on a computer using the Bessel, Hankel, and Mueller and Gauss methods.
The considered problems were reduced to finding complex natural frequencies for the system of equations of motion of a cylindrical shell in an infinite viscoelastic medium using radiation conditions. It is shown that the problem has a discrete complex spectrum. The eigen frequencies of oscillations of a low-contrast heterogeneity are found. Revealed that the imaginary part of the eigen frequencies is comparable with the real one, which can lead to aperiodic movements of the systems considered.
This article was devoted to the development of methods of the dynamic calculation based on the finite difference method of laminar structures in the framework of the bimoment theory, which takes into account the spatial stress-strain state. Were given the solutions of the problem of transverse vibrations of the plate model of structures.
The results of calculations of the enclosing dam stability of phosphogypsum sludge collectors are presented in the paper. The stability calculations were carried out according to the “RUZO” program; they are based on the method of circular-cylindrical sliding surfaces under the action of basic and seismic loads. The main objective of this work is to determine the minimum safety factors for dam slopes of a given transverse profile under known loads and characteristics of the dam body material. To develop a rational profile of collector dams, 9 options of design models of the structure and its base were considered. The body of the enclosing dams of collectors of considered options consists, as a rule, of two elements: the primary floodwall built of earth materials, and secondary dams constructed according to a different build-up schemes from stored materials. Secondary dams are constructed from stored phosphogypsum by the method of layer-by-layer filling and compaction. The calculations showed that in all considered schemes the minimum safety factors under the action of basic and seismic loads are higher than the standard values. The maximum permissible values of the slopes are established with an allowable margin of safety, thus, the stability of dam slopes in all considered options of the phosphogypsum collector is ensured under basic and special combinations of loads.
The paper provides a detailed analysis of the current state of the problem. A mathematical model is presented to determine the dynamic behavior of earth dams, considering the viscoelastic properties of soil, using the hereditary Boltzmann-Volterra theory with the A.R. Rzhanitsyn kernel under periodic kinematic impacts. To solve the problems considered, the finite element method and complex arithmetics were used to reduce integrodifferential equations to a high-order complex algebraic equation. The accuracy of the methods was verified by solving test problems. Steadystate forced vibrations of the Pskem earth dam 195 m high are studied considering the real geometry and soil properties under resonant vibration modes. It was stated that the largest stress amplitudes in the body of the dam occur not only under the first resonance, but they can occur under other dense spectra of the eigenfrequencies of the dam, due to the interaction between close natural modes of vibration. The strength of various sections of the dam body was tested under kinematic impact using the Coulomb- Mohr theory of strength; the most dangerous sections of the dam were identified in terms of the highest stress.
An industrial waste-phosphogypsum-is formed in the production of phosphorus mineral fertilizers. As is well-known, the issues of processing and utilization of phosphogypsum on an industrial scale remain unsolved. Consequently, production waste generated at chemical plants is stored in various types of storage tanks. The currently used hydraulic storage method provides for the supply of waste in the form of a slurry into the hydraulic dump cells, their sequential dehydration in the dump, and the subsequent development of a part of the stored waste for the construction of secondary dams. However, due to the low water-release properties of phosphogypsum, it is impossible to ensure its dehydration to the required degree, in large volumes, and the required period. Therefore, various designs of watertight diaphragms and drainage devices are provided in the sludge collector to accelerate the process of dehydration of the phosphogypsum strata. The balance of the sludge collector should be assessed in two periods: the initial period when the sludge collector cells are filled, bounded by the primary dam, and the subsequent period when the reservoir is built up by erecting secondary dams from the stored material. In the initial period, the operating mode of the sludge collector is divided into two stages: in the first stage, a pond is formed above the layer of sludge with a certain predetermined depth; in the second stage, this depth of water in the pond is kept constant by the spillways. The second build-up period is preceded by a period of cell preparation, namely: the draw-off of the pond and drainage of the cell to a moisture content suitable for the dam filling and normal operation of the mechanisms used in the construction of dams. This article presents the results of filtration studies in sludge collectors with an impermeable screen (made of polymer film, asphalt-polymer concrete, etc.) above the screen drainage system. The calculating methods for the determination of filtration parameters in the second period of operation are described: when the pulp supply stops, and a pond of clarified water with a depth of H0 is drawn off.
The article is devoted to improving the model of a box-like structure of a building, taking into account the forces and moments in the zones of contact interaction of beam and plate elements. The equations of motion of the box-like elements, the boundary conditions in the base of the box and the contact conditions between the elements of the box are given; the graphs of panels and beams displacements are constructed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.