scholarly journals MATHEMATICAL SIMULATION OF THE SYSTEM SEISMIC FLUCTUATIONS, WHICH CONSISTS OF THE TAILINGS DUMP EMBANKMENT DAM, THE MATERIAL OF DEPOSIT (TAILS) AND UNDER BOTTOM GROUND LAYERS

2016 ◽  
Author(s):  
И.Д. Музаев
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Seismic Wave Propagation ◽  
Contact Boundary ◽  
Embankment Dam ◽  
Seismic Vibrations ◽  
Contact Surfaces ◽  
The Mathematical Model

Разработана математическая модель совместных сейсмических колебаний системы, состоящей из дамбы обвалования хвостохранилища, материала отложения (хвосты) и подподошвенных слоев грунтового массива. Модель представляет собой контактную краевую задачу для дифференциального уравнения сдвигово-вязких поперечных колебаний тела дамбы с материалами отложений, а также для дифференциальных уравнений сдвигово-вязких поперечных колебаний слоев массива грунта. Эти уравнения взаимосвязаны через граничные условия на контактных поверхностях. Краевая задача решена аналитически. Получены расчетные формулы для вычисления перемещений, скорости и ускорения тела дамбы при распространении падающей на систему сейсмической волны в слоях грунта и в теле дамбы The mathematical model of the system seismic vibrations, which consists of the tailings dump embankment dam, the material of deposit (tails) and under botto ground layers is developed. Model is contact boundary-value problem for the differentialequation of the dam body shift- viscous lateral oscillations with the materials of deposits, and also for the differential equations of the shift- viscous lateraloscillations of the ground layers. These equations are interconnected through the boundary conditions on the contact surfaces. Boundary-value problem is solved analytically. Calculation formulas for enumerating of displacements, velocity and acceleration calculation of the dam body with the seismic wave propagation in the ground layers and into in the dam body.

scholarly journals MATHEMATICAL MODELING OF SEISMIC VIBRATIONS OF THE DAM AND UNDERFOUNDATION LAYERS OF THE SOIL MASSIF TAKING INTO ACCOUNT THE INFLUENCE OF WATER IN THE RESERVOIR

2017 ◽  
Author(s):  
Н.И. Музаев ◽  
К.С. Харебов ◽  
И.Д. Музаев
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
High Pressure ◽  
Seismic Waves ◽  
Mathematical Physics ◽  
Contact Boundary ◽  
Influence Of Water ◽  
Seismic Vibrations ◽  
The Mathematical Model ◽  
Oscillatory Processes

Составлена математическая модель совместных сейсмических колебаний высоконапорной плотины, водохранилища и двух слоев массива грунта под основаниями плотины и водохранилища. Модель представляет контактную краевую задачу математической физики в которой учтены взаимозависимости колебательных процессов в грунтовой толще, в плотине и в водохранилище при распространении гармонической сейсмической волны в рассматриваемой системе. В результате решения поставленной задачи получены расчетные формулы для вычисления относительных амплитуд сейсмических колебаний гребня и основания плотины. The mathematical model of the co-seismic vibrations of high-pressure dams, reservoirs and two layers of soil under the foundations of the dam and reservoir is created. The model represents the contact boundary value problem of mathematical physics which takes into account the interdependence of oscillatory processes in soil, in the dam and in the reservoir during the propagation of harmonic seismic waves in the system under consideration. As a result of solving the tasks the formulae are derived to calculate the relative amplitudes of the oscillations of the top and the base of the dam.

scholarly journals AMPLITUDE – FREQUENCY CHARACTERISTICS OF SEISMIC IMPACT ON THE BUILDING WITH THE GROUND BASE AND THE COMPARISON OF THEORETICAL ESTIMATION WITH THE REAL EVENTS FROM THE DA TA BASE SMDB CGI

2015 ◽  
Author(s):  
К.С. Харебов ◽  
И.Д. Музаев ◽  
Н.И. Музаев
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Ground Surface ◽  
Frequency Characteristics ◽  
Contact Boundary ◽  
Soil Layers ◽  
Reflected Waves ◽  
Seismic Vibrations ◽  
Seismic Impact

В статье поставлена и решена многослойная контактная краевая задача сейсмических колебаний системы, состоящей из упруго-вязких слоев под застройкой. Краевая задача состоит из nдифференциальных уравнений описывающих поперечные сдвиговые колебания слоев грунта. На каждой поверхности контакта слоев грунта дифференциальные уравнения взаимосвязаны двумя граничными условиями, выражающими равенство перемещений и касательных напряжений в смежных слоях грунта. Последний глубинный слой считается полуограниченным. На бесконечности ставится условие ограниченности перемещения и частных производных перемещения. Поставленная краевая задача решена методом суперпозиции прямых и отраженных волн.Получены расчетные формулы для амплитуд сейсмических колебаний каждого слоя, в том числе и для дневной поверхности. Составлена соответствующая программа расчета на компьютере. Проведена расчетная оценка частотных характеристик грунта при сейсмическом воздействии. Проведено сравнение результатов расчетов с частотными параметрами реальных землетрясений на реальных площадках. The multilayer contact boundary-value problem of the seismic vibrations of the system, consisting of the elastic-viscous layers under the building, is set and solved. Boundary-value problem consists of n differential equations describing transversalshear vibrations of soil layers. On each contact surface of soil layers differential equations are interconnected by two boundary conditions, which express the equality of displacements and shearing stresses in the adjacent of soil layers. The last deep layer is considered semi-bounded. At infinity the limitedness of displacement and partial derivatives of displacement is stipulated.The presented boundary-value problem is solved by the method of the forward and reflected waves superposition. Calculation formulas for the seismic vibrations amplitudes of each layer, including for the ground surface are obtained.The corresponding program of calculation on the computer is created. The frequency characteristics evaluation of the seismic impact on the building is carried out. The comparison of results with the parameters of real earthquakes from the data base SMDB CGI is carried out.

scholarly journals The Mathematical Modeling of Metals Mass Transfer in Three Layer Peat Blocks

2015 ◽  
Vol 1 ◽  
pp. 87
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Mathematical Models ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Difference Methods ◽  
The Mathematical Model

The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.

scholarly journals Simulation of the process of water purification in multilayered micro porous media

2019 ◽  
pp. 61-63
Author(s):  
Olena Prysiazhniuk ◽  
Andrii Safonyk ◽  
Anna Terebus
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Boundary Value Problem ◽  
Water Purification ◽  
Asymptotic Approximation ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
The Mathematical Model ◽  
Purification Of Water

The mathematical model of the process of adsorption purification of water from impurities in multilayer microporous filters is formulated. An algorithm for numerically-asymptotic approximation of solution of the corresponding nonlinear singularly perturbed boundary value problem is developed. The developed model allows to investigate the distribution of concentration of pollutant inside the filer.

THE STABILITY AND FREE VIBRATIONS OF A COLUMN SUBJECTED TO A CONSERVATIVE LOAD GENERATED BY A HEAD WITH A PARABOLIC CONTOUR

2013 ◽  
Vol 13 (07) ◽  
pp. 1340012
Author(s):  
LECH TOMSKI ◽  
SEBASTIAN UZNY
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Free Vibrations ◽  
Specific Load ◽  
Kinetic Criterion ◽  
The Stability ◽  
The Mathematical Model ◽  
First Time ◽  
Roller Radius

The boundary value problem concerning the free vibrations of a slender system subjected to a specific load has been formulated and solved in this work. Heads with parabolic contour have been used to realize the specific load for the first time. The boundary value problem has been formulated using Hamilton's principle. The critical load and the characteristic curves in the plane load–natural frequency have been determined on the basis of the kinetic criterion of stability. Numerical calculations have been assigned to different values of the parameters of the considered system for which the parabolic parameter and the parameter of the roller radius are ranked. The roller is the head of the receiving load. The accuracy of the mathematical model was confirmed on the basis of experimental research based on frequency and modal analysis.

scholarly journals Boundary Value Problem of an Infinite Array of Loaded Apertures

2015 ◽  
Vol 3 ◽  
pp. 11-15
Author(s):  
Luis Alejandro Iturri-Hinojosa ◽  
Alexander E. Martynyuk ◽  
Mohamed Badaoui
Keyword(s):  
Mathematical Model ◽  
Reflection Coefficient ◽  
Plane Wave ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Incident Plane Wave ◽  
Incident Plane ◽  
Infinite Array ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model of the scattering by a periodically arranged apertures in conducting plates is presented. The boundary value problem of an infinite array of loaded apertures is formulated for an arbitrary incident plane wave. The reflection coefficient for some array geometries is obtained and the calculated values are in good agreement with the measurements in a previously published researches. All the rectangular apertures in the array are assumed to be identical and infinitesimally thin. The mathematical model is based on Floquet’s theorem that specifies the requirement of periodicity by the electromagnetic fields.

scholarly journals Research of a mathematical model of low-concentrated aqueous polymer solutions

2006 ◽  
Vol 2006 ◽  
pp. 1-27 ◽  
Author(s):  
Mikhail V. Turbin
Keyword(s):  
Mathematical Model ◽  
Weak Solution ◽  
Boundary Value Problem ◽  
Polymer Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Aqueous Polymer ◽  
Initial Boundary Value ◽  
The Mathematical Model

The initial-boundary value problem for the mathematical model of low-concentrated aqueous polymer solutions is considered. For this initial-boundary value problem a concept of a weak solution is introduced and the existence theorem for such solutions is proved.

A New Method and Applications of the Boundary Value Problem of Differential Equation

2014 ◽  
Vol 937 ◽  
pp. 695-699
Author(s):  
Hong E Li ◽  
Xiao Xu Dong ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Cong Yin Fan
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Kernel Function ◽  
Boundary Value ◽  
Outer Boundary ◽  
Seepage Flow ◽  
Petroleum Engineering ◽  
Constructive Method ◽  
Linear Homogeneous Differential Equation ◽  
The Mathematical Model

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

Mathematical model implementation in conditions of uncertainty and possible risks

2021 ◽  
pp. 137-145
Author(s):  
A. Kravtsov ◽  
◽  
D. Levkin ◽  
O. Makarov ◽  
◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Layer Structure ◽  
Boundary Value ◽  
Goal Function ◽  
Cauchy Problems ◽  
System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

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