scholarly journals STUDY OF STABILITY OF A TANK-CONTAINER WITH A FILLED LIQUID AT LONGITUDINAL OSCILLATIONS

2020 ◽  
Vol 6 (444) ◽  
pp. 228-235
Author(s):  
V. G. Solonenko ◽  
◽  
N. M. Makhmetova ◽  
V. A. Nikolaev ◽  
M. Ya. Kvashnin ◽  
...  
Keyword(s):  
Differential Equations ◽  
Dynamic Stability ◽  
Theoretical Calculations ◽  
System Of Differential Equations ◽  
Longitudinal Vibrations ◽  
Hydrodynamic Problem ◽  
Main Method ◽  
The Stability

The effect of the oscillating fluid on the dynamic stability of the tank-container is studied at different filling capacities. The main method for studying the dynamic stability of a railway platform with a tank- container in theoretical calculations is the method of full integration, i.e. all the solutions of the system of differential equations describing the movement of the tank-container with liquid are found, and from them a conclusion is made on the stability of the movement. The study of the longitudinal vibrations of the liquid and the tank-container is considered at various impact speeds and without taking into account the galloping angle. The solution of the system of differential equations reduces to the solution of the hydrodynamic problem.

scholarly journals A New L-Stable Third Derivative Hybrid Method for Solving First Order Ordinary Differential Equations

2021 ◽  
pp. 58-69
Author(s):  
Lawrence Osa Adoghe
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Multistep Method ◽  
Stability And Convergence ◽  
Stiff Systems ◽  
Convergence Properties ◽  
Main Method ◽  
The Stability ◽  
Third Derivative

In this paper, an L-stable third derivative multistep method has been proposed for the solution of stiff systems of ordinary differential equations. The continuous hybrid method is derived using interpolation and collocation techniques of power series as the basis function for the approximate solution. The method consists of the main method and an additional method which are combined to form a block matrix and implemented simultaneously. The stability and convergence properties of the block were investigated and discussed. Numerical examples to show the efficiency and accuracy of the new method were presented.

scholarly journals Dynamic Model of Growing File-Sharing P2P Network

2019 ◽  
Vol 26 (3) ◽  
pp. 351-359
Author(s):  
Alexandra I. Kononova ◽  
Larisa G. Gagarina
Keyword(s):  
Differential Equations ◽  
Dynamic Model ◽  
Information Exchange ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
System Of Differential Equations ◽  
First Approximation ◽  
The Stability ◽  
General Provision ◽  
Exchange Network

In this work, the model of development of the P2P file exchange network organized by a torrent tracker is considered. The model is constructed on the basis of ordinary differential equations. The phase variables describing a status of a torrent tracker and the network organized by it (in first approximation is the number of the users of the tracker who are actively participate in information exchange, and the number of active torrents) are defined, the factors influencing the change of users number and the number of torrents are analyzed. On the basis of the analysis the system of differential equations, in first approximation describing evolution of the file exchange network organized by the torrent tracker — a hard dynamic model of evolution of the torrent tracker is written. Equilibrium points of hard model of evolution of the tracker are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a hard model of evolution of the torrent tracker are described. The phase portrait of the hard model is represented. On the basis of the analysis of the hard model the system of differential equations describing evolution of a file exchange network with accounting of dependence of new users inflow intensity on a total quantity of potential audience of the torrent tracker, and also dependences of speed of torrents extinction on the number of users falling on one torrent — a soft dynamic model of evolution of a torrent tracker is written. Equilibrium points of a soft model of tracker evolution are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a soft model of evolution of the torrent tracker are described. Phase portraits of each configuration are represented. The ratio of parameters necessary for the stability of the tracker a stable status is received. The influence of different administrative measures on a stock of the tracker stability in whole is analyzed. The need of support of torrents by administration at highly specialized torrent trackers with small potential audience is shown.

scholarly journals Bifurcation and stability of periodic solutions from a zero eigenvalue

1979 ◽  
Vol 21 (1) ◽  
pp. 2-20
Author(s):  
K. A. Landman
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Double Zero ◽  
Zero Eigenvalue ◽  
Time Periodic Solutions ◽  
The Stability ◽  
Bifurcation And Stability ◽  
Time Periodic

AbstractA study is made of the branching of time periodic solutions of a system of differential equations in R2 in the case of a double zero eigenvalue. It is shown that the solution need not be unique and the period of the solution is large. The stability of these solutions is analysed. Examples are given and generalizations to larger systems are discussed.

scholarly journals ДИНАМІЧНА РЕАКЦІЯ ТА СТІЙКІСТЬ ПОШКОДЖЕНОЇ КОНСТРУКЦІЇ ТРАНСПОРТНОГО ЛІТАКА

2020 ◽  
pp. 173-180
Author(s):  
Є. Ю. Іленко ◽  
В. М. Онищенко
Keyword(s):  
Dynamic Stability ◽  
Equations Of Motion ◽  
Initial Perturbation ◽  
Aerodynamic Characteristics ◽  
Operating Conditions ◽  
Ultimate State ◽  
Main Method ◽  
Operating Load ◽  
The Stability

In the process of designing and operating the aircraft, it is important to determine the ultimate state of the structure, taking into account the dynamic load of the structure and its stability. The ultimate state of the structure is characterized by damage, in which the structure still retains the ability to withstand without catastrophic destruction of the maximum operating load. The main method of studying the stability of the structure is the dynamic method. It allows us to investigate the perturbed motion of a structure as a nonconservative system for some initial perturbation. The monotonic departure of the system from the equilibrium position or its oscillations with increasing amplitudes indicate the instability of the structure. The paper analyzes the effect of damage to the aircraft structure on its dynamic stability based on the determination of the dynamic response of the aircraft to some non-stationary perturbation, for example, on the action of a turbulent atmosphere. The method of computational analysis is used to study the dynamic stability of the structure. The basis of this method is mathematical modeling (MM) of the operation of the aircraft in the form of a system of equations of motion and deformation of the structure. The problem of dynamic aeroelasticity is considered - the behavior of the elastic damaged structure of the aircraft in the air flow to the initial perturbation. On the basis of computer simulation, the dynamic stability of the elastic structure, its oscillating or quasi-static (aperiodic) deformation motion within the flight range of the aircraft is estimated. On the basis of parametric researches the limits of instability of a design at the set damages for typical operating conditions are estimated. The relevance of the direction focused on the creation and advanced operation of MM aircraft - their mathematical backups in the process of design and operation of aircraft due to the complexity and limited capabilities of ground experimental installations and flight experiment. It is noted that the condition for the application of this method is the formed MM operation of the aircraft and the availability of information on the mass-inertial, stiffness and aerodynamic characteristics of the aircraft.

scholarly journals MODEL MATEMATIKA KEARIFAN LOKAL MASYARAKATDESA TRUSMI DALAM MENJAGA EKSISTENSIKERAJINAN BATIK TULIS

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Arif Muchyidin
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Numerical Simulation ◽  
National Identity ◽  
Differential Equations ◽  
Critical Point ◽  
Critical Points ◽  
System Of Differential Equations ◽  
The Stability ◽  
The Village

Batik as an Indonesian national identity has contributed greatly to the Indonesian economy. However, the value of exports and other economic potentials are not supported by the number of batik, especially batik artisans in the village Trusmi. Trusmi batik artisans in the village is a craftsman who has been there all the time and remain there for generations. The phenomenon that occurs in the craft of batik Trusmi analyzed with mathematical modeling approach, in this case the dynamical system. From the resulting system of differential equations, then analyzed the stability around the critical point. From the resulting model, gained two critical points. The first critical point is a condition where there is no proficient craftmen (not expected), whereas at the second critical point is the potential of batik craftmen and proficient craftmen mutually exist, or in other words batik will still exist. From the results of numerical simulation, if , then batik Trusmi will still exist. However, if , then the number of proficient craftmen would quickly dwindle and slowly batik will be extinct.Key Words : dinamical system, critical points, stability

scholarly journals The stability of geometrically nonlinear plate systems under the action of dynamic loads

2020 ◽  
Vol 16 (3) ◽  
pp. 219-225
Author(s):  
Sergey P. Ivanov ◽  
Anastasia S. Ivanova ◽  
Oleg G. Ivanov
Keyword(s):  
Differential Equations ◽  
Dynamic Stability ◽  
Dynamic Compression ◽  
Nonlinear Differential Equations ◽  
Longitudinal Direction ◽  
Geometrically Nonlinear ◽  
Nonlinear Plate ◽  
Prismatic Shell ◽  
The Stability ◽  
Plate System

Relevance. Single-connected and multi-connected plate systems are widely used in construction, aircraft, shipbuilding, mechanical engineering, instrument making. As a result, the study of the stability of geometrically nonlinear plate systems is an urgent topic. But, despite significant achievements in this area, there are still many unsolved problems. Thus, the requests of the above-mentioned areas of application of thin-walled spatial systems require further study of the issue of static and dynamic stability. The aim of the work - development of a method of the dynamic stability analysis of geometrically nonlinear plate systems such as prismatic shells under the action of dynamic compression loads. Methods. A plate system, which is subject to dynamic compression loads in the longitudinal direction, is considered. Kirchhoff - Love hypotheses are taken into account. The material stress-deformation diagram is linear. The displacement of points in the normal direction to the median plane of the plates is determined in the form of the Vlasov expansion. To derive the basic differential equations of stability, the energy method and the variational Vlasov method are used. The extreme value of the total energy is determined using the Euler - Lagrange equation. As a result, a set of basic nonlinear differential equations for studying the buckling of the plate system under the action of dynamic compression loads is obtained. Results. The developed method is used to stability analysis of a geometrically nonlinear prismatic shell with a closed contour of the cross section, under central compression under the action of dynamic loading. The edges of the shell rest on the diaphragm. The buckling of the prismatic shell in the longitudinal direction along one and two half-waves of a sinusoid is studied. The numerical integration of nonlinear differential equations is performed by the Runge - Kutta method. Based on the calculation results, graphs of the dependence of the relative deflection on the dynamic coefficient are constructed. The influence of the rate of change of compression stress, the initial imperfection of the system, and other parameters on the criteria for the dynamic stability of the plate system is investigated.

Dynamic Stability of a Pendulous Missile Suspension System

1962 ◽  
Vol 29 (2) ◽  
pp. 276-282
Author(s):  
V. Chobotov
Keyword(s):  
Differential Equations ◽  
Dynamic Stability ◽  
Periodic Coefficient ◽  
Suspension System ◽  
Second Order ◽  
Stability Criteria ◽  
Parametrically Excited ◽  
Second Order Differential Equations ◽  
The Stability

The stability criteria for a missile on a pendulous support are derived for the case of parametrically excited motions of the support. The suspension system is described by two linear second-order differential equations with a periodic coefficient. The analysis is carried out by means of the first method of Liapunov. The results are somewhat modified, however, to obtain greater generality without which the technique is too laborious to be useful.

scholarly journals On Fractional Order Dengue Epidemic Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hamed Al-Sulami ◽  
Moustafa El-Shahed ◽  
Juan J. Nieto ◽  
Wafa Shammakh
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Fractional Order ◽  
Epidemic Model ◽  
System Of Differential Equations ◽  
The Stability ◽  
Disease Free ◽  
Dengue Epidemic

This paper deals with the fractional order dengue epidemic model. The stability of disease-free and positive fixed points is studied. Adams-Bashforth-Moulton algorithm has been used to solve and simulate the system of differential equations.

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