scholarly journals Wave concept of motion in mathematical models of the dynamics of two-dimensional media studying

2019 ◽  
Vol 5 (3-4) ◽  
pp. 8-15
Author(s):  
Andrij Andrukhiv ◽  
◽  
Bohdan Sokil ◽  
Mariia Sokil ◽  
◽  
...  
Keyword(s):  
Mathematical Models ◽  
Asymptotic Methods ◽  
Wave Theory ◽  
Single Frequency ◽  
Two Dimensional ◽  
Klein Gordon ◽  
Basic Parameters ◽  
The Impact ◽  
The Mathematical Model ◽  
The Waves

The methodology of the studying of dynamic processes in two-dimensional systems by mathematical models containing nonlinear equation of Klein-Gordon was developed. The methodology contains such underlying: the concept of the motion wave theory; the single - frequency fluctuations principle in nonlinear systems; the asymptotic methods of nonlinear mechanics. The aggregate content allowed describing the dynamic process for the undisturbed (linear) analogue of the mathematical model of movement. The value determining the impact of nonlinear forces on the basic parameters of the waves for the disturbed analogue is defined.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ УДАРУ ПРУЖНОГО ЛІТАЛЬНОГО АПАРАТА НА ПОСАДЦІ

2019 ◽  
pp. 165-169
Author(s):  
В. М. Онищенко
Keyword(s):  
Mathematical Models ◽  
Aerodynamic Characteristics ◽  
Impact Dynamics ◽  
Elastic Plane ◽  
Actual Problem ◽  
Parametric Studies ◽  
Basic Parameters ◽  
Experimental Facilities ◽  
Basic Equations ◽  
The Impact

The development of a direction oriented towards the creation and advanced operation of mathematical models (MM) of aircraft - their mathematical doublers on the example of calculating the impact dynamics and loading of an elastic plane on landing is shown. The relevance of such an approach in the design and operation of aircraft due to the complexity and limited capabilities of terrestrial experimental facilities and flight experiment are noted. The example of a lightweight aircraft presents the results of the application of a simplified MM and the numerical calculation of the impact dynamics on the computer and the load of the elastic construction at landing. Determination of the dynamic reaction of the aircraft and the load of the elastic structure at landing refers to the actual problem of dynamic aeroelasticity. In the article the basic equations used to construct the MM of an elastic plane with a nonlinear landing gear are given. The basic parameters that characterize the structural load are determined. The results of the calculation analysis of the impact of the aircraft are presented, extensive parametric studies have been carried out on the influence of a number of constructive and operational factors on dynamic processes, and analyzed the patterns and features of impact and loading of an elastic aircraft on landing. It is shown that the load must be determined taking into account elastic structural vibrations. Dynamic loads from elastic oscillations are significant in magnitude and, as it turns out, most often determine the strength of the glider and the chassis. It is emphasized that the condition of the application of the calculated method is the mathematical models of the operation of the aircraft and the availability of information on the aircraft  – mass-inertial, rigid and aerodynamic characteristics.

scholarly journals The Mathematical Model for Research of the UAV Longitudinal Moving

2021 ◽  
Vol 13 (5) ◽  
pp. 29-39
Author(s):  
Sergii Zhdanov ◽  
◽  
Natalia Kadet ◽  
Valerii Silkov ◽  
Mariia Zirka ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Frequency Response ◽  
Unmanned Aerial Vehicles ◽  
Control Systems ◽  
Aerial Vehicles ◽  
General Mathematical Model ◽  
Logarithmic Frequency ◽  
The Impact ◽  
The Mathematical Model

The paper presents one of the perspective directions of the development to modern aviation, which is connected with designing and producing unmanned aerial vehicles (UAV) of various functionalities for applying in both military and civilian spheres. The syntheses of UAV control systems, regardless of their type and purpose presumes creation of adequate mathematical models, first of all adequate aerodynamic mathematical models. In the paper results that forms and justify the aerodynamic mathematical model and as well as the results of building a general mathematical model of the longitudinal movement of the perspective UAV are presented. Also factors that forms the mathematical model on given aerodynamic, geometric, mass and inertial data for a hypothetical perspective altitude long-range UAV are submitted. Assessment of the impact of these data on the dynamic, temporal, and logarithmic frequency response UAV also has been given in this paper.

Ultrasonic Characteristics of the Ultrasonic Grinding Process about the Nano-Ceramic Plate

2011 ◽  
Vol 418-420 ◽  
pp. 1690-1693 ◽  
Author(s):  
Ming Zhang ◽  
Yu Qing Wang ◽  
Feng Jiao
Keyword(s):  
High Efficiency ◽  
Skin Effect ◽  
Wave Theory ◽  
Ultrasonic Waves ◽  
Grinding Process ◽  
Ceramic Plate ◽  
Two Dimensional ◽  
Ultrasonic Grinding ◽  
The Waves ◽  
Order Surface

In this paper, the sand vibration test of the ultrasonic wave is done under ultrasonic vibration grinding. In this test, the "skin effect"is observed when the ultrasonic waves pass to the nano-ceramic plate, which is amplified by the ultrasonic horn. This phenomenon is analyzed by the second-order surface wave theory and the waves which pass to the workpiece are surface waves generated. These explain the good grinding surface quality and high efficiency under the two-dimensional ultrasonic grinding in the same conditions.

Ultrasonic Vibration Characteristics of Nano-Composite Ceramic in the Ultrasonic Polishing Process

2012 ◽  
Vol 522 ◽  
pp. 147-151
Author(s):  
Ming Zhang ◽  
Feng Jiao
Keyword(s):  
Surface Waves ◽  
High Efficiency ◽  
Three Dimensional ◽  
Wave Theory ◽  
Composite Ceramic ◽  
Ceramic Plate ◽  
Two Dimensional ◽  
Nano Composite ◽  
The Waves ◽  
Order Surface

The ultrasonic polishing test of the nanoZrO2-Al2O3composite ceramics is done under the two-dimensional ultrasonic polishing device, which is developed by us. In this process, the ultrasonic amplitude-frequency characteristic testing is done by the DASP software. There are certain amplitudes at some frequency points, which can be seen from the spectrum and the three-dimensional spectral array maps, but only one the largest amplitude appears. This shows the resonance points appear when the ultrasonic is passed to the nanocomposite ceramic plate after it is amplified by the horn. This phenomenon is analyzed by the second-order surface wave theory and the waves are surface waves, which are generated by surface waves. These explain the good polishing surface quality and high efficiency under the two-dimensional ultrasonic polishing in the same conditions.

A Note on the Evaluation of the Wave Resistance of Two-Dimensional Bodies from Measurements of the Downstream Wave Profile

1983 ◽  
Vol 27 (02) ◽  
pp. 90-92
Author(s):  
James H. Duncan
Keyword(s):  
Wave Train ◽  
Wave Theory ◽  
Stokes Wave ◽  
Two Dimensional ◽  
Third Order ◽  
The Subject ◽  
Lord Kelvin ◽  
The Waves ◽  
The Vertical Distribution

As a body moves horizontally at constant speed in the proximity of a free surface it experiences a resistance due to the generation of waves. In two-dimensional cases the determination of this resistance from properties of the wave train has been the subject of several investigations. The linear theory was first presented by Lord Kelvin [1] 2 and later by Havelock [2] and Lamb [8]. Wehausen and Laitone [4] have derived an exact resistance formula in terms of the vertical distribution of velocity in the waves and the downstream surface height profile. This formula was later evaluated by Salvesen and von Kerczek [5] using third-order Stokes wave theory.

One-Dimensional Impact Waves in Inhomogeneous Elastic Media

1969 ◽  
Vol 36 (4) ◽  
pp. 803-808 ◽  
Author(s):  
Edward L. Reiss
Keyword(s):  
Asymptotic Methods ◽  
Variable Coefficients ◽  
Elastic Media ◽  
One Dimensional ◽  
Klein Gordon ◽  
Inhomogeneous Elastic Media ◽  
Impact Problems ◽  
Impact Data ◽  
The Impact ◽  
Impact Problem

Several one-dimensional impact problems for inhomogeneous elastic media are reduced by suitable transformations of variables to three different canonical forms. One of them is the impact problem for the wave equation with variable sound speed. Another, which we call Problem I, is the impact problem for the Klein-Gordon equation with variable coefficients. Several methods of approximating the solution of Problem I are discussed. The wave front approximation is obtained by assuming that sufficiently near the discontinuity propagating from the impacted boundary the solution has a Taylor series in time. The coefficients in the series are the time derivatives of the solution evaluated on the discontinuity. They are obtained from an analysis of the propagation of the discontinuity using the theory of weak solutions. A formal asymptotic expansion of the solution is obtained for oscillatory impact data. Reflections from boundaries are also considered. Perturbation methods for media with slowly varying inhomogeneities and asymptotic methods for media with rapidly varying inhomogeneities are briefly discussed.

Solow economy model

2019 ◽  
pp. 150-157
Author(s):  
Oleksandr Synenko ◽  
Kateryna Yarema ◽  
Yuliia Bezsmertna
Keyword(s):  
Economic Growth ◽  
Regression Analysis ◽  
Solow Model ◽  
Economy Model ◽  
Accelerated Depreciation ◽  
Basic Parameters ◽  
The Subject ◽  
Investment Process ◽  
The Impact ◽  
Model Algorithm

The subject of the research is the approach to the possibility of using the Solow model to perform the regression analysis on the example of the Ukrainian economy model. The purpose of writing this article is to investigate the notion of regres- sion analysis, Solow’s economy model, algorithm for performing regression analy- sis on the example of Ukraine’s economy model. This model can be adapted for the economy of enterprises. Methodology. The research methodology is system-struc- tural and comparative analyzes (to study the structure of GDP); monograph (when studying methods of regression analysis on the example of the Ukrainian economy); economic analysis (when assessing the impact of factors on Ukraine’s GDP). The scientific novelty consists the features of the use of the Solow model on the ex- ample of Ukrainian economy are determined. An algorithm for calculating the basic parameters of a model using the Excel application package is disclosed. The main recommendations on the development of the national economy and economic growth through the use of macroeconomic instruments are given. Conclusions. The use of the Solow model enables forecasting and analysis. The results obtained re- vealed the problem of low resource return of capital as a resource, along with the means of macroeconomic regulation of the investment process, using which can improve the situation. A special place in these funds belongs to the accelerated depreciation and interest rate policies.

Recent Advances and Need of Green Synthesis in Two-Dimensional Materials for Energy Conversion and Storage Applications

2021 ◽  
Vol 16 ◽  
Author(s):  
Joice Sophia Ponraj ◽  
Muniraj Vignesh Narayanan ◽  
Ranjith Kumar Dharman ◽  
Valanarasu Santiyagu ◽  
Ramalingam Gopal ◽  
...  
Keyword(s):  
Energy Storage ◽  
Green Synthesis ◽  
2D Materials ◽  
Synthesis Method ◽  
Energy Storage And Conversion ◽  
Two Dimensional ◽  
Severe Problem ◽  
Energy Conversion And Storage ◽  
Energy Application ◽  
The Impact

: Increasing energy crisis across the globe requires immediate solutions. Two-dimensional (2D) materials are in great significance because of its application in energy storage and conversion devices but the production process significantly impacts the environment thereby posing a severe problem in the field of pollution control. Green synthesis method provides an eminent way of reduction in pollutants. This article reviews the importance of green synthesis in the energy application sector. The focus of 2D materials like graphene, MoS2, VS2 in energy storage and conversion devices are emphasized based on supporting recent reports. The emerging Li-ion batteries are widely reviewed along with their promising alternatives like Zn, Na, Mg batteries and are featured in detail. The impact of green methods in the energy application field are outlined. Moreover, future outlook in the energy sector is envisioned by proposing an increase in 2D elemental materials research.

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