scholarly journals Mathematical Modelling of Tank Wagon Vibrations Considering Partially Filling of the Tank with Liquid Cargo

2021 ◽  
Vol 19 (2) ◽  
pp. 25-30
Author(s):  
P. S. Grigoriev ◽  
S. N. Korzhin ◽  
Sh. R. Ibodulloev ◽  
Phu Thuan Tran
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Differential Equations ◽  
Mathematical Modelling ◽  
Dynamic Characteristics ◽  
Angular Displacement ◽  
Lagrange’S Equation ◽  
Kinetic And Potential Energies

Mathematical modelling of processes of motion makes it possible to assess the dynamic characteristics of a wagon at the stage of its design. However, it is necessary to consider the type of cargo transported, the movement of which affects the values of these features.The paper considers a mathematical model of an eight-axle railway tank wagon developed using the Lagrange’s equation of the second kind. The considered mathematical model suggests an approach based on the consideration of the influence of the energy of a liquid cargo in a steady state of motion. This influence was considered by evaluating the kinetic and potential energies of vibrations of the transported liquid cargo.Differential equations of vibration compiled for the model under consideration represent the liquid cargo as a solid. The approach for considering the effect of liquid cargo during vibrations of a tank wagon assumes that the total volume of the displaced liquid approximately corresponds to the volume of the layer of the fluid determined by displacement of bouncing, or in the case of galloping, with an angular displacement of one end section of the tank wagon, the second section rises by the same value, in other words, we observe the system of communicating vessels. Based on these assumptions, energy additions are obtained that consider movement of a liquid cargo under steady-state modes of motion.According to the proposed approach, preliminary calculations were performed, and the results obtained were assessed. The results obtained showed satisfactory convergence with the calculations carried out using other approaches to modelling of the processes of movement of railway tank wagons. 

scholarly journals Deployment/Retrieval Modeling of Cable-Driven Parallel Robot

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Q. J. Duan ◽  
J. L. Du ◽  
B. Y. Duan ◽  
A. F. Tang
Keyword(s):  
Mathematical Model ◽  
Boundary Condition ◽  
Steady State ◽  
Differential Equations ◽  
Parallel Robot ◽  
Lumped Mass ◽  
Dynamic Motion ◽  
Long Span ◽  
System A ◽  
Lumped Mass Method

A steady-state dynamic model of a cable in air is put forward by using some tensor relations. For the dynamic motion of a long-span Cable-Driven Parallel Robot (CDPR) system, a driven cable deployment and retrieval mathematical model of CDPR is developed by employing lumped mass method. The effects of cable mass are taken into account. The boundary condition of cable and initial values of equations is founded. The partial differential governing equation of each cable is thus transformed into a set of ordinary differential equations, which can be solved by adaptive Runge-Kutta algorithm. Simulation examples verify the effectiveness of the driven cable deployment and retrieval mathematical model of CDPR.

INFLUENCE OF SUBSTRATE LOADING AND DETACHMENT CONDITIONS ON A PLANE BIOFILM BEHAVIOUR

2013 ◽  
Vol 34 (4) ◽  
pp. 463-477
Author(s):  
Michał Blatkiewicz ◽  
Bolesław Tabiś ◽  
Stanisław Ledakowicz
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Differential Equations ◽  
Process Parameters ◽  
Live Cell ◽  
The Other ◽  
Cell Distribution ◽  
Single Substrate ◽  
Influence Of Substrate ◽  
Substrate Kinetics

Abstract A mathematical model of a plane, steady state biofilm, with the use of a single substrate kinetics, was proposed. A set of differential equations was solved. In order to analyse the biofilm’s behaviour, a number of simulations were performed. The simulations included varying process parameters such as detachment coefficient and substrate loading. Two detachment models were taken into consideration: one describing the detachment ratio as proportional to the thickness of the biofilm, and the other one proportional to the thickness of the biofilm squared. The results provided information about substrate and live cell distribution in biofilm and the influence of certain parameters on biofilm behaviour.

Mathematical modeling of articulated passenger train spatial vibrations

2021 ◽  
Vol 2021 (2) ◽  
pp. 91-99
Author(s):  
O. Markova ◽  
◽  
H. Kovtun ◽  
V. Maliy ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Ride Quality ◽  
Railway Transport ◽  
Passenger Train ◽  
Wide Range ◽  
Random Track Irregularities ◽  
The Mathematical Model

The problem of high-speed railway transport development is important for Ukraine. In many countries articulated trains are used for this purpose. As the connections between cars in such a train differ from each other, to investigate its dynamic characteristics not a separate car, but a full train vibrations model is necessary. The article is devoted to the development of the mathematical model for articulated passenger train spatial vibrations. The considered train consists of 7 cars: one motor-car, one transitional car, three articulated cars, one more transitional car and again one motor-car. Differential equations of the train motion along the track of arbitrary shape are set in the form of Lagrange’s equations of the second kind. All the necessary design features of the vehicles are taken into account. Articulated cars have common bogies with adjoining cars and a transfer car and the cars are united by the hinge. The operation of the central hinge between two cars is modeled using springs and dampers acting in the horizontal and vertical directions. Four dampers between two adjacent car-bodies act as dampers for pitching and hunting and are represented in the model by viscous damping. The system of 257 differential equations of the second order is set, which describes the articulated train motion along straight, curved, and transitional track segments with taking into account random track irregularities. On the basis of the obtained mathematical model the algorithm and computational software has been developed to simulate a wide range of cases including all possible combinations of parameters for the train elements and track technical state. The study of the train self-exited vibrations has shown the stable motion in all the range of the considered speeds (40 km/h – 180 km/h). The results obtained at the train motion along the track maintained for the speedy motion have shown that all the dynamic characteristics and ride quality index insure train safe motion and comfortable conditions for the travelling passengers.

A Mathematical Model for Close Coil Current Signal Analysis

2013 ◽  
Vol 325-326 ◽  
pp. 552-555
Author(s):  
Yu Huang Zheng
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Dynamic Characteristics ◽  
Signal Analysis ◽  
Dynamic State ◽  
Control Law ◽  
Current Signal ◽  
Circuit Breakers ◽  
Coil Current ◽  
Simulation And Experiment

The focus of this paper centers on the analysis of the close coil current signal in circuit breakers (CBs). The characteristic behavior of the close coil is analyzed by the electromagnet control law and a mathematical model is made to describe the dynamic characteristics of the close coil. Results of simulation and experiment are presented in the form of curves of the current of the close coil. The results show that the accuracy of the steady-state and dynamic-state model is satisfactory.

scholarly journals Dissolution of an ensemble of differently shaped poly-dispersed drug particles undergoing solubility reduction: mathematical modelling

ADMET & DMPK ◽  
2020 ◽  
Author(s):  
Michela Abrami ◽  
Lucia Grassi ◽  
Rosario Di Vittorio ◽  
Dritan Hasa ◽  
Beatrice Perissutti ◽  
...  
Keyword(s):  
Phase Transition ◽  
Mathematical Model ◽  
Differential Equations ◽  
Mathematical Modelling ◽  
Size Distribution ◽  
Research Community ◽  
Dissolution Process ◽  
Liquid Environment ◽  
Particles Size Distribution ◽  
Theoretical Paper

<p class="ADMETabstracttext">The aim of this theoretical paper is to develop a mathematical model for describing the dissolution process, in a finite liquid environment, of an ensemble of poly-dispersed drug particles, in form of sphere, cylinder and parallelepiped that can undergo solubility reduction due to phase transition induced by dissolution. The main result of this work consists in its simplicity as, whatever the particular particles size distribution, only two ordinary differential equations are needed to describe the dissolution process. This, in turn, reflects in a very powerful and agile theoretical tool that can be easily implemented in electronic sheets, a widespread tool among the research community. Another model advantage lies on the possibility of determining its parameters by means of common independent techniques thus enabling the evaluation of the importance of solid wettability on the dissolution process.</p>

scholarly journals Deterministic chaos in pendulum systems with delay

2019 ◽  
Vol 4 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Aleksandr Shvets ◽  
Alexander Makaseyev
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Differential Equations ◽  
Deterministic Chaos ◽  
Phase Portraits ◽  
Characteristic Exponents ◽  
Systems Of Differential Equations ◽  
Lyapunov Characteristic Exponents ◽  
The Mathematical Model ◽  
Equations With Delay

AbstractDynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".

scholarly journals Steady-state modelling and performance of a rotary direct drive digital valve

2020 ◽  
Vol 53 (3-4) ◽  
pp. 311-319
Author(s):  
Yuesong Li
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Angular Displacement ◽  
Stepper Motor ◽  
Direct Drive ◽  
Rotary Valve ◽  
Steady State Flow ◽  
Load Pressure ◽  
State Flow ◽  
The Relationship

A rotary direct drive digital valve driven by a stepper motor was proposed. By analysing its working principle, the steady-state mathematical model reflecting the relationship between the pressure, the flow and the angular displacement was deduced. Based on this mathematical model, the models of the null valve coefficients, the zero leakage flow and the steady-state flow torque were given. The simulation shows that the relationship between the pressure and the flow of the rotary valve is nonlinear; however, under a constant load pressure, the flow characteristics and the steady-state flow torque characteristics of the rotary valve with rectangular throttle orifices are linear. The experimental results show that the flow is directly proportional to the steps of the stepper motor, and the proposed mathematical models are valid.

scholarly journals Mathematical modeling of the functioning process of a single-cylinder air-cooled diesel engine taking into account the consumption of crankcase gases

2020 ◽  
Vol 1 (3) ◽  
pp. 75-82
Author(s):  
D.V. Pavlov ◽  
◽  
K.Yu. Platonov ◽  
R.N. Khmelev ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Diesel Engine ◽  
Differential Equations ◽  
Internal Combustion Engines ◽  
Computational Experiment ◽  
Working Fluid ◽  
Engine Operation ◽  
Single Cylinder ◽  
The Mathematical Model

At present, the most effective method for studying internal combustion engines (ICE) is mathe-matical modeling and computational experiment. The use of a computational experiment can signif-icantly reduce material and time costs in the research, design and refinement of the internal combus-tion engine. At the same time, despite the high level of the applied mathematical models, there are practically no studies aimed at establishing the regularities of the influence of the state of the cylin-der-piston group (CPG) on the crankcase gas consumption and other indicators of engine operation at steady-state and transient modes. This article is devoted to solving an urgent problem associated with the development of a theoretical base that provides a comprehensive simulation of steady-state and transient modes of diesel engine operation, taking into account the consumption of crankcase gases. The article presents a mathematical model of a diesel engine based on thermal mechanics, which reflects the main features of the engine as a system that converts energy in time. The system of equations of the mathematical model is based on the laws of conservation of energy, mass, equa-tions of motion of solid links and includes differential equations for the rates of change in the tem-perature and density of the working fluid in the cylinder and in the crankcase of the internal com-bustion engine, the ideal gas equation of state, as well as differential equations for the change in the angular speed and angle of motor shaft rotation. The mathematical model is tested on the example of a small-sized single-cylinder diesel engine 1Ch9.5 / 8.0 with air cooling. This type of engine is widely used for small-scale mechanization in agriculture, generator sets, etc. The article presents the results of calculations of a number of engine operating modes in comparison with the results of field tests carried out at the test bench.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

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