
Keyword: "stability"
Petr Aleksandrovich Velmisov, Doctor of Sciences in Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles and monographs in the field of aerohydromechanics, aerohydroelasticity, mathematical modeling. email: velmisov@ulstu.ru.P. Velmisov,
Iulia Valerevna Pokladova, Candidate of Sciences in Physics and Mathematics, Associate Professor; graduated from the Faculty of Economics and Mathematics of Ulyanovsk State Technical University; Associate Professor of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles and monographs in the field of aerohydroelasticity, mathematical modeling. email: pokladovau@inbox.ru.I. Pokladova,
Mizher Usama Jawad, Postgraduate Student at the Department of Higher Mathematics of UlSTU; graduated from the University of ThiQar, College of Engineering Governorate, Bachelor (Iraq, ThiQar); Vladimir Dahl East Ukrainian National University, Master’s program (Ukraine, Lugansk); an author of articles in the field of aerodynamics, aerohydroelasticity, mathematical modeling. email: usama.mizher@gmail.com.M. Jawad


Mathematical Modeling Of Nonlinear Dynamics Of the Pipeline
In the work, various nonlinear mathematical models are proposed that describe pipeline vibrations. Models are presented that take into account only the transverse deformation of the pipeline, and models that take into account the longitudinal and transverse deformations. All models are described by partial differential equations for unknown strain functions. The numericalanalytical solution is based on the BubnovGalerkin method. Based on model equations, a numerical experiment was conducted for various parameters of a mechanical system, which showed a small difference in dynamic characteristics for different models. A functional of the Lyapunov type was constructed for one of the models, on the basis of which the analytical conditions for the dynamic stability of the pipeline were obtained. Also, mathematical models of the dynamics of the pipeline are proposed taking into account the delay of power and (or) inertial characteristics. Pipeline, deformation, dynamics, stability, nonlinear model, partial differential equations, Lyapunov functional method.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Vladimir Nikolaevich Kliachkin, Ulyanovsk State Technical University, Doctor of Engineering; graduated from the Mechanical Faculty of Ulyanovsk Polytechnic Institute; Professor at the Department of Applied Mathematics and Informatics of Ulyanovsk Polytechnic University; an author of scientific works in the field of reliability and statistical methods. [email: v_kl@mail.ru]V. Kliachkin, Irina Nikolaevna Karpunina, Ulyanovsk Institute of Civil Aviation named after Chief Marshal of Aviation B.P. Bugaev, Candidate of Engineering, Associate Professor; graduated from Moscow Aviation Institute; Associate Professor at the Department of General Professional Disciplines at Ulyanovsk Institute of Civil Aviation named after Chief Marshal of Aviation B.P. Bugaev; interested in dynamics and strength of machines, reliability. [email: karpunina53@yandex.ru]I. Karpunina, Mariia Konstantinovna Fedorova, Ulyanovsk State Technical University, graduated from the Faculty of Information Systems and Technologies of Ulyanovsk State Technical University; interested in computeraided technologies of statistical data analysis. [email: mashulka3031_94@mail.ru]M. Fedorova


Evaluation of the Computer Temperature Regime Stability
The temperature regime significantly affects the durability of the computer. Ensuring stability of the computer functioning considers the stability of the heating temperature of the main elements that should not exceed the specified values. The article discusses issues related to the timely warning about a possible violation of the temperature regime stability. In order to diagnose stability, the multivariate statistical control methods are proposed to use. Evaluation of stability is carried out with the use of two criteria: stability of the temperature average level and their dispersion. Independent parameters can be controlled with the use of standard shewhart charts. The algorithms on the basis of Hotelling statistics (for assessing stability of the middlelevel temperature measurement process) and generalized variance (for evaluation of the dispersion process stability) are used for correlated parameters. The efficiency of these algorithms can be enhanced through the analysis of nonrandom structures on the control charts, the use of the warning border, as well as application of modifications based on the cumulative amounts or moving averages weighted exponentially. The multivariate statistical technique of the computer temperature regime control including monitoring in the context of a welldeveloped process for a training sample in order to separate the parameters controlled for a group of independent and correlated ones, process analysis for assessment of control characteristics and continuous monitoring of the process with the construction of Hotelling charts and generalized dispersion with identifying possible violations of the process based on the presence of significant structures and the use of a warning border. This technique is illustrated by the example of five computer temperature regime parameters control. Stability, temperature, hotelling algorithm, warning limit, generalized variance, control chart.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Automated control systems, Electrical engineering and electronics. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’; an author of monographs, articles, and a textbook in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Optimization of Hierarchical Control System Stability
Designing of hierarchical control systems with optimal stability indices in condition of price limitation is considered in the article. The formal description of hierarchical system structure and functioning algorithm was made. The choice of optimal solution comes to the operational research on the basis of analytic dependencies between system stability indices and objects stability ones. In order to plot the analytic dependence, the authors propose to approximate the experimental data got in simulation process. The simulation model was made with the use of MonteCarlo method. The paper proposes approximate formula models including orthogonal transformation reducing given dependencies to simple approximate forms. The possibility of direct application of scarce resources distribution search with the increasing performance of computer aids for the purpose of optimizing stability indices of the system is demonstrated. On the base of simulation, optimizing software has been developed. Also the article presents the calculation results that prove reasonability of direct application of simulation models in systems of special class. Stability, hierarchical computeraided control systems, optimal design, simulation.



Sections: Automated control systems
Subjects: Automated control systems. 
Petr Alexandrovich Velmisov, Ulyanovsk State Technical University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles and monographs in the field of aerohydromechanics, aerohydroelasticity, and mathematical modeling. [email: velmisov@ulstu.ru]P. Velmisov, Sergei Vladimirovich Kireev, Ulyanovsk State Technical University, Candidate of Physics and Mathematics; graduated from the Faculty of Mechanics and Mathematics of Moscow State University (Branch at Ulyanovsk); Associate Professor at the Department of Higher Mathematics of Ulyanovsk State Technical University; an author of articles and a monograph in the field of aerohydroelasticity and mathematical modeling. [email: ksv1511@yandex.ru]S. Kireev


Numerical Method for Solving a Class of Nonlinear Boundary Value Problems of Aerohydroelastity
On the basis of nonlinear models proposed and a numerical method developed for solving corresponding boundary value problems in nonlinear integrodifferential equations static instability (divergence) of the pipeline with the fluid flowing in it is investigated. A numerical method for solving the bifurcation problem includes the RungeKutta 6th order method with the error control at each step, Newton's method for solving nonlinear equations and integration with the use of NewtonKotesa quadrature formulas. Solving the boundary value problem is reduced to solving a Cauchy problem. The complexity of a Cauchy problem is that there is an integral term in the equation. Calculation of this term needs values of the whole integration interval. It makes the direct application of the RungeKutta method impossible. To solve this problem (integration) a special iterative process was developed. Numerical realization is provided with the use of a program written in Delphi 7. Bifurcation diagrams showing the dependence between maximal element bending and the inflow velocity are obtained. Moreover, the element’s forms of deflection are specified. The obtained numerical solutions were compared with analytical ones. Stability, divergence, elastic element, pipeline, nonlinear model, differential equations, boundary value problem, mathematical modeling, numerical method.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Petr Alexandrovich Velmisov, Ulyanovsk State Technical University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles and monographs in the field of aerohydromechanics, aerohydroelasticity, and mathematical modeling. [email: velmisov@ulstu.ru]P. Velmisov, Andrei Viktorovich Korneev, Ulyanovsk State Technical University, graduated from the Faculty of Information Systems and Technologies at Ulyanovsk State Technical University; PostGraduate Student at the Department of Higher Mathematics of Ulyanovsk State Technical University; an author of articles in the field of aerohydroelasticity, optimal control, and algorithms development. [email: a.korneev1@gmail.com]A. Korneev


Mathematical Modeling in the Problem of Dynamic Stability of a Pipeline
The paper presents mathematical models for a viscoelastic pipeline that is a hollow rod containing flowing the fluid (gas). The article is devoted to the problem of the dynamic stability of a pipeline. Linear and nonlinear models describe partial differential equations for an unknown function (the displacement of the pipeline points from the equilibrium state). By means of Lyapunov functionals designed stability theorems are formulated and analytical stability conditions for the parameters of the mechanical system and different types of initial conditions are found. The obtained stability conditions are sufficient but not necessary. A mathematical software package is developed to solve this problem. It allows to find an approximate numerical solution of differential equation for describing pipeline vibration and to plot a stability area appropriate to both sufficient and necessary stability conditions. A numerical experiment of stability areas designing is conducted on the basis of the software package. The obtained numerical results are interpreted and compared with analytical stability conditions. The influence of the model parameters variation on the stability is researched. Mathematical modeling, viscoelastic pipeline, aerohydroelasticity, stability, functional, partial differential equations, numerical methods, galerkin method.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Andrey Vladimirovich Ankilov, Ulyanovsk State Technical University, Candidate of Physics and Mathematics; graduated from the Faculty of Mechanics and Mathematics of Moscow State University (Branch at Ulyanovsk); Associate Professor at the Department of Higher Mathematics of Ulyanovsk State Technical University; an author of articles and monographs in the field of mathematical modeling, aerohydroelasticity. [email: ankil@ulstu.ru]A. Ankilov, Petr Aleksandrovich Velmisov, Ulyanovsk State Technical University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles, textbooks, and monographs in the field of mathematical modeling, aerohydroelasticity, aerohydrodynamics, differential equations. [email: velmisov@ulstu.ru]P. Velmisov


Dynamics and Stability of Elastic Aileron of Aircraft Wing in Subsonic Streamline
A mathematical model of a wing with the aileron blown by a subsonic flow of the ideal gas (fluid) is offered. It is supposed that the wing is absolutely rigid, and the aileron is elastic. Dynamics and dynamic stability of the aileron are investigated. The model is described by a related system of partial differential equations for two unknown functions: the potential of velocity of gas coming on the wing and deformations of the elastic aileron. Based on the methods of the theory of functions of complex variable, the potential of velocity is expelled from the system of equations and the solution of a problem of aerohydroelasticity is consolidated to a research of the integrodifferential equation containing only an unknown function of deformation of the elastic aileron. It is supposed that thickness of the elastic aileron is a variable that results in a system of equations with variable coefficients. A study of stability is performed on basis of creation of positively certain functionality corresponding to the received partial integrodifferential equation. The stability conditions imposing restrictions on velocity of the incoming flow, thickness, flexural rigidity of the aileron and on other parameters of the mechanical system are received. The solution of the specified integrodifferential equation for function of deformation of an element relies on basis of the Galerkin method with carrying out a numerical experiment. Aerohydroelasticity, stability, dynamics, elastic element, wing, aileron, subsonic flow.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Andrey Vladimirovich Ankilov, Ulyanovsk State Technical University, Candidate of Physics and Mathematics; graduated from the Faculty of Mechanics and Mathematics of Moscow State University (Branch at Ulyanovsk); Associate Professor at the Department of Higher Mathematics of Ulyanovsk State Technical University; an author of articles and monographs in the field of mathematical modeling, aerohydroelasticity. [email: ankil@ulstu.ru]A. Ankilov, Petr Aleksandrovich Velmisov, Ulyanovsk State Technical University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles, textbooks, and monographs in the field of mathematical modeling, aerohydroelasticity, aerohydrodynamics, and differential equations. [email: velmisov@ulstu.ru]P. Velmisov, Yulia Alexandrovna Tamarova, Ulyanovsk Instrument Manufacturing Design Bureau JSC, graduated from the Faculty of Mechanics and Mathematics of Ulyanovsk State University; Software engineer of Ulyanovsk Instrument Manufacturing Design Bureau JSC; an author of articles in the field of mathematical modeling, aerohydroelasticity, aerohydrodynamics. [email: kazakovaua@mail.ru]Y. Tamarova


The Dynamical Stability of an Elastic Element of the Flow Channel
A mathematical model of a device pertaining to the vibration equipment which is intended for intensification of technological processes, for example, stirring process, is offered. Operation of such devices is based on fluctuations of elastic elements blown by a flow of gas or fluid. The dynamic stability of an elastic element placed on one of the walls of the channel where a subsonic flow of gas or fluid blows (in a model of ideal compressible medium) is investigated. The model is described by a related system of partial differential equations for two unknown functions: the potential of velocity of gas or fluid and deformation of the elastic element. The problem is investigated in a linear statement corresponding to small perturbations of the flow in the channel and small deformations of the elastic element. Determination of the stability of the elastic body corresponds to a concept of stability of dynamical systems by Lyapunov. Based on building of the mixed functional, sufficient conditions of stability are obtained. Conditions impose limitations on the speed of the uniform gas flow, compressed (tensile) efforts of the element, elastic element stiffness and other parameters of the mechanical system. Examples of building stability areas for concrete parameters of the mechanical system are given. Aerohydroelasticity, stability, dynamics, channel, elastic plate, deformation, subsonic flow.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Ivanovich Moiseev, FRPC OJSC 'RPA 'Mars', Candidate of Engineering, graduated from the Dual Degree Faculty at Ulyanovsk State University; a lead programmer at FRPC OJSC 'RPA 'Mars'; is majoring in the field of design of specialpurpose control systems; an author of papers, inventions and registered software systems in the field of research and building of specialpurpose distributed control systems. [email: mars@mv.ru]A. Moiseev, Vladimir Viktorovich Kalnikov, FRPC OJSC 'RPA 'Mars', Candidate of Engineering, Associate Professor, graduated from the RadioEngineering Faculty at Kiev Higher Military School of Communications named after M.I. Kalinin, finished his postgraduate studies of the same School; a chief specialist at FRPC OJSC 'RPA 'Mars'; his major is the design of specialpurpose control systems; an author of papers, manuals and inventions in the field of design of specialpurpose distributed control systems, communications and dataexchange systems. [email: mars@mv.ru]V. Kalnikov


Analysis of the State of a Distributed Control System
Abstract The article examines an issue about how to estimate the current state of distributed control systems with the analytical models obtained as for indices of secrecy, information awareness and stability. When estimating the secrecy of control, the emission time and the amplitude of the signal of a giveaway sign are taken into account. It is suggested to calculate the information awareness of operations posts with the weapons under their control using the entropic approach. The obtained results of the mathematical expression have the parameters for the required observation accuracy, errors, acquisition range, and the information update rate included. We have developed statistical and dynamic variants for such a characteristic of a distributed control system. It is suggested to analyze the control stability along with the estimation of survivability, reliability and noiseresistance of operations posts. The average number of data transmission paths, bandwidth ratio and its assignment evenness, the operations posts’ average load and its assignment evenness are chosen as the private parameters for the control survivability. A recurrent algorithm for the appropriate graph conversion and analysis is suggested to estimate the system reliability. The control noiseresistance is represented as a quantity derivative of the noise probability and the probability of an operation post to keep its performance ability. State, distributed control systems, combat readiness, secrecy, information awareness, stability, estimation.



Sections: Automated control systems
Subjects: Automated control systems, Architecture of ship's system. 
Petr Alexandrovich Velmisov, Ulyanovsk State Technical University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles, textbooks, and monographs in the field of mathematical modeling, aerohydroelasticity, aerohydrodynamics, differential equations. [email: velmisov@ulstu.ru]P. Velmisov, Sergey Vladimirovich Kireev, Ulyanovsk State Technical University, Candidate of Physics and Mathematics; graduated from the Faculty of Mechanics and Mathematics of Moscow State University (Branch at Ulyanovsk); Associate Professor at the Department of Higher Mathematics of Ulyanovsk State Technical University; an author of articles and a monograph in the field of aerohydroelasticity and mathematical modeling. [email: ksv1511@yandex.ru]S. Kireev


Mathematical Modelling in Instability Problems of Elastic Structural Elements in Gas Flow
On the basis of the proposed nonlinear models and developed numerical method for the solution to the corresponding nonlinear boundaryvalue problems, the static instability (divergence) of the elastic element of the design streamlined and supersonic flow of ideal gas is investigated. A numerical procedure for the bifurcationproblem solution includes the 6th order RungeKutta method with the error control at the step, the Newton's method required for solving nonlinear equations, and integration using NewtonKotesa quadrature. The solution to the boundaryvalue problem is reduced to the Cauchy problem solution, the complexity of which is that the integral term is present in the equation. In order to calculate this integral term the values of the integrand function on the whole interval of integration are required. It makes impossible the direct application of the RungeKutta Method. A special iterative process was developed to solve this problem as integral evaluation. Numerical implementation is carried out by the program written in Delphi 7. Bifurcation diagrams are given that showing the maximal element dependence on incident stream velocity. Element bendingforms are defined. The comparison of obtained numerical solutions against analytical solutions is carried out. The dynamic stability of the elastic structural element in a supersonic gas flow is researched by the Galerkin’s method. The element bending dependences on time in a fixed point are obtained. Stability, divergence, elastic element, plate, supersonic flow, nonlinear model, differential equations, boundaryvalue problem, mathematical modelling, numerical method.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Vladimir Vasilyevich Sukhov,
A Way of Modeling of Strength and Vibrationprotection Systemsfor Radio Devices Vladimir Vasilyevich Sukhov, Joint StockCompany Concern 'MorinformsystemAgat' (Moscow), Candidate of Engineering, graduated from the Faculty of Mechanical Engineering of Bauman Moscow State Technical University in the profession 'Radiomechanical Devices'; leading staff scientist;
author of articles, holds patents in the field of trials and calculations of dynamics and strength of radio equipment, system of vibration isolation, vibroacoustic and noise characteristics, thermal conditions [email: vsuhov51@yandex.ru]V. Sukhov


A Way of Modeling of Strength and Vibrationprotection Systemsfor Radio Devices
Optimization of vibroprotection systems for radio devices is an essential element for increase of reliability and strength. Under permanent increase in prices of similar equipment, modeling of its mechanical strength at all the design stages lets ensure compliance with reliability requirements and replace mechanical trials of devices with modeling. Radio equipment, vibroprotection, device design, modeling, strength, stability.



Sections: Mathematical modeling, calculi of approximationsandsoftware systems
Subjects: Mathematical modeling, Electrical engineering and electronics. 

Calculation of Eigenvalues and Eigenvectors By Jacobi Method At Variable Capacity
The article deals with possible increase of rate of convergence of eigenvalue and eigenvector calculation by Jacobi method. The method is based on change of capacity of original variables in case of stable
state approximation. In general, the suggested method is more advantageous with respect to direct implementation. Iteration process, jacobi method, variable capacity, stability.



Sections: Theoretical issues of automation of command and control processes
Subjects: Mathematical modeling. 
