Pub Date : 2021-02-16DOI: 10.33842/2313-125X/2021/20/48/59
A. Brailov, V. Panchenko
model for the most general relative location of the location of the geodetic equipment and the investigated object. 2. Development of a structure of mathematical foundations for the processing of experimental data obtained in the determination of parameters of an inaccessible point using the developed three-dimensional geometrical model with crossed directional rays. 3. Development of the content of each structural block of the developed mathematical foundations. Efficiency of the developed combined geometrical model is in verified in the course of the solution of the problem of determination of coordinates of two inaccessible points C and C', located on a perpendicular to horizontal plane П 1 . The mathematical foundations structurally consist of seven blocks. The content of each structural block corresponds to the developed optimizing analytical model of determination of domain (area) of values of the parameters of an inaccessible point of an object.
{"title":"MATHEMATICAL-ALGORITHMIC ADAPTIVE FOUNDATION FOR SOLVING THE PROBLEM OF DETERMINING OF THE PARAMETERS OF AN INACCESSIBLE OBJECT","authors":"A. Brailov, V. Panchenko","doi":"10.33842/2313-125X/2021/20/48/59","DOIUrl":"https://doi.org/10.33842/2313-125X/2021/20/48/59","url":null,"abstract":"model for the most general relative location of the location of the geodetic equipment and the investigated object. 2. Development of a structure of mathematical foundations for the processing of experimental data obtained in the determination of parameters of an inaccessible point using the developed three-dimensional geometrical model with crossed directional rays. 3. Development of the content of each structural block of the developed mathematical foundations. Efficiency of the developed combined geometrical model is in verified in the course of the solution of the problem of determination of coordinates of two inaccessible points C and C', located on a perpendicular to horizontal plane П 1 . The mathematical foundations structurally consist of seven blocks. The content of each structural block corresponds to the developed optimizing analytical model of determination of domain (area) of values of the parameters of an inaccessible point of an object.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130204279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-16DOI: 10.33842/2313-125X/2021/20/68/75
V. Vereshchaga, Y. Adoniev
The article proposes a composite geometric method for analysis of information in Big Data sets at the stage of their primary processing and “cleaning”. The method is based on the methods of the Baluba-Naydysh point calculus is a preparatory stage when using the structural geometric modelling of Big Data. the minimal use of machine resources when working with Big Data significantly reduces the cost of obtaining valuable conclusions and forecasts.
{"title":"COMPOSITIONAL GEOMETRIC METHOD OF INFORMATION ANALYSIS AND ITS APPLICATION WHEN WORKING WITH BIG DATA","authors":"V. Vereshchaga, Y. Adoniev","doi":"10.33842/2313-125X/2021/20/68/75","DOIUrl":"https://doi.org/10.33842/2313-125X/2021/20/68/75","url":null,"abstract":"The article proposes a composite geometric method for analysis of information in Big Data sets at the stage of their primary processing and “cleaning”. The method is based on the methods of the Baluba-Naydysh point calculus is a preparatory stage when using the structural geometric modelling of Big Data. the minimal use of machine resources when working with Big Data significantly reduces the cost of obtaining valuable conclusions and forecasts.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129542852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-08DOI: 10.33842/2313-125X/2020/19/95/101
O. Kravets
The use of economic-mathematical apparatus, through the mathematical model construction of optimization of the sizes of the raw material base of processing enterprises is lighted in the article. Economic efficiency of any enterprise depends on many factors, one of which is а quality management. The overall economic performance of the company largely depends on the efficiency, timeliness and quality of decision-making. One of the tools helping to solve these problems is the wide use of mathematical apparatus, which provides the opportunity not only to perform the necessary calculations, but also to systematize, justify and simulate the behavior of an object in a particular production situation. According to the analysis of research and publications, relevance of the question of creation economico-mathematical model of optimization of the sizes of the raw material base of processing enterprises is very important, therefore, we propose to create a mathematical model that would allow taking into account various economic factors, to predict the processing plants profit, according to one or another managerial decision. The implementation of an appropriate model will enable the management to determine the optimum amount of acreage that will provide the company, according to technological opportunities and market capacity, necessary raw materials for production; ensure the quality and timeliness of management decision making, through a systematic approach to the consideration of the most important factors affecting the efficiency of production; reduce the time spent on calculations, provided that a matrix of tasks and the use of modern software products; can be used to predict and compare the possibility of obtaining the optimum financial and economic performance results when changing macro and micro economic factors, influencing on economic efficiency of production.
{"title":"MODELING IN MANAGEMENT OF ECONOMIC SYSTEMS IN PROCESS PLANTS","authors":"O. Kravets","doi":"10.33842/2313-125X/2020/19/95/101","DOIUrl":"https://doi.org/10.33842/2313-125X/2020/19/95/101","url":null,"abstract":"The use of economic-mathematical apparatus, through the mathematical model construction of optimization of the sizes of the raw material base of processing enterprises is lighted in the article. Economic efficiency of any enterprise depends on many factors, one of which is а quality management. The overall economic performance of the company largely depends on the efficiency, timeliness and quality of decision-making. One of the tools helping to solve these problems is the wide use of mathematical apparatus, which provides the opportunity not only to perform the necessary calculations, but also to systematize, justify and simulate the behavior of an object in a particular production situation. According to the analysis of research and publications, relevance of the question of creation economico-mathematical model of optimization of the sizes of the raw material base of processing enterprises is very important, therefore, we propose to create a mathematical model that would allow taking into account various economic factors, to predict the processing plants profit, according to one or another managerial decision. The implementation of an appropriate model will enable the management to determine the optimum amount of acreage that will provide the company, according to technological opportunities and market capacity, necessary raw materials for production; ensure the quality and timeliness of management decision making, through a systematic approach to the consideration of the most important factors affecting the efficiency of production; reduce the time spent on calculations, provided that a matrix of tasks and the use of modern software products; can be used to predict and compare the possibility of obtaining the optimum financial and economic performance results when changing macro and micro economic factors, influencing on economic efficiency of production.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116972543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-08DOI: 10.33842/2313-125X/2020/19/154/162
D. Spirintsev, A. Naydysh, V. Fomenko, V. Spirintsev
An analysis of the known methods of continuous geometric modeling showed that they rely on a predetermined class of functions. This leads to the replacement of the differential-geometric characteristics of the DPC by the characteristics of these functions and does not exclude the influence of the properties of the modeling function on the simulation result. Discrete interpolation methods are deprived of the above drawbacks, which, in addition to guaranteeing the absence of oscillations and having wide possibilities for local solution correction, have the simplicity of computational algorithms and their software implementation. There is a wide variety of discrete geometric modeling methods that allow you to solve the problem of thickening of the duodenum of arbitrary shape. These methods differ in complexity and versatility in solving applied problems of geometric modeling. Among the well-known methods of discrete interpolation, a separate direction should be distinguished variable discrete geometric modeling (VDGM) [1], the defining feature of which is that as a result of modeling not one parameter value is calculated, but the interval of its admissible values, from which the desired one is selected, optimal in the sense of the problem, the value of the parameter. One of the methods of VDGM is the method of variably forming difference schemes of angular parameters, the distinguishing feature of which is that it uses angular parameters in the process of condensation, as well as that which is equally effective for convex (concave) DPC, and DPC with features in geometry. However, like most existing methods, in its practical application not only the main algorithm of the method is used, but also its modifications depending on the type of condensed sections (concave, convex, contain transitional or rectilinear sections, singular points). Therefore, for the practical use of this method, it was necessary to develop a general scheme of the method, which in the future will increase the efficiency of its application.
{"title":"GENERAL SCHEME OF THE METHOD OF VARIATIVE FORMATION OF DIFFERENT SCHEMES OF ANGULAR PARAMETERS","authors":"D. Spirintsev, A. Naydysh, V. Fomenko, V. Spirintsev","doi":"10.33842/2313-125X/2020/19/154/162","DOIUrl":"https://doi.org/10.33842/2313-125X/2020/19/154/162","url":null,"abstract":"An analysis of the known methods of continuous geometric modeling showed that they rely on a predetermined class of functions. This leads to the replacement of the differential-geometric characteristics of the DPC by the characteristics of these functions and does not exclude the influence of the properties of the modeling function on the simulation result. Discrete interpolation methods are deprived of the above drawbacks, which, in addition to guaranteeing the absence of oscillations and having wide possibilities for local solution correction, have the simplicity of computational algorithms and their software implementation. There is a wide variety of discrete geometric modeling methods that allow you to solve the problem of thickening of the duodenum of arbitrary shape. These methods differ in complexity and versatility in solving applied problems of geometric modeling. Among the well-known methods of discrete interpolation, a separate direction should be distinguished variable discrete geometric modeling (VDGM) [1], the defining feature of which is that as a result of modeling not one parameter value is calculated, but the interval of its admissible values, from which the desired one is selected, optimal in the sense of the problem, the value of the parameter. One of the methods of VDGM is the method of variably forming difference schemes of angular parameters, the distinguishing feature of which is that it uses angular parameters in the process of condensation, as well as that which is equally effective for convex (concave) DPC, and DPC with features in geometry. However, like most existing methods, in its practical application not only the main algorithm of the method is used, but also its modifications depending on the type of condensed sections (concave, convex, contain transitional or rectilinear sections, singular points). Therefore, for the practical use of this method, it was necessary to develop a general scheme of the method, which in the future will increase the efficiency of its application.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130285586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-08DOI: 10.33842/2313-125X/2020/19/117/123
A. Nezenko, S. Kozlov
Features of reproducing aircraft design geometric parameters during the production stage analyzed in the presented study. Problematic issues highlighted on unit production and aircraft final assembly due to the influence of various objective and subjective factors on variations of geometric parameters of a product. Such factors can be fluctuations in the ambient temperature, internal stresses of the material, the accumulation of errors, and inaccuracies in design calculations, et cetera. Lines determined for comprehensive solutions of problems on geometric parameters variations by creating a sequence of geometric models with actual geometric parameters using the concept of a digital twin. It was demonstrated that the geometric model sequence of aircraft outer contours is an integral component of its digital twin and the basis for the designing of models of different technical paths. It was proposed to apply the methodology of structural-parametric modeling using approaches of process-based geometric modeling to create the sequence of geometric models of an aircraft digital twin. It was demonstrated that approaches to the creation of geometric models of a product actual geometric parameters at the production stage are different from methods used for geometric modeling at the steps of research and development. A number of the main issues were considered that facing the design and technological departments when creating models of actual geometric parameters of aircraft units at each stage of its production. The general directions were determined for further research of geometric modeling methods to solve the problems of changing geometric parameters during the manufacturing of aircraft. The materials presented serve as the basis for the development of appropriate geometric models and software tools for computer-aided design.
{"title":"GEOMETRIC MODELING IN THE ASPECT OF PRODUCT DIGITAL TWIN CONCEPT","authors":"A. Nezenko, S. Kozlov","doi":"10.33842/2313-125X/2020/19/117/123","DOIUrl":"https://doi.org/10.33842/2313-125X/2020/19/117/123","url":null,"abstract":"Features of reproducing aircraft design geometric parameters during the production stage analyzed in the presented study. Problematic issues highlighted on unit production and aircraft final assembly due to the influence of various objective and subjective factors on variations of geometric parameters of a product. Such factors can be fluctuations in the ambient temperature, internal stresses of the material, the accumulation of errors, and inaccuracies in design calculations, et cetera. Lines determined for comprehensive solutions of problems on geometric parameters variations by creating a sequence of geometric models with actual geometric parameters using the concept of a digital twin. It was demonstrated that the geometric model sequence of aircraft outer contours is an integral component of its digital twin and the basis for the designing of models of different technical paths. It was proposed to apply the methodology of structural-parametric modeling using approaches of process-based geometric modeling to create the sequence of geometric models of an aircraft digital twin. It was demonstrated that approaches to the creation of geometric models of a product actual geometric parameters at the production stage are different from methods used for geometric modeling at the steps of research and development. A number of the main issues were considered that facing the design and technological departments when creating models of actual geometric parameters of aircraft units at each stage of its production. The general directions were determined for further research of geometric modeling methods to solve the problems of changing geometric parameters during the manufacturing of aircraft. The materials presented serve as the basis for the development of appropriate geometric models and software tools for computer-aided design.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115929512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-08DOI: 10.33842/2313-125X/2020/19/163/178
K. Fomina
The purpose of studying geometry is the development of spatial abilities. However, sometimes it is difficult for beginners to perceive two-dimensional images representing three-dimensional space in the learning process. Augmented reality is a technology that has demonstrated its effectiveness in learning and can be used to create didactic materials. Its feature is the placement of a virtual object in a real environment, in real-time and considering the location in space. Complementing the real environment with virtual information, it helps the user solve real-world problems. Despite the benefits, novelty, and interest in technology in the field of education, there are very few studies that demonstrate practical implementation and how to use it in the study of geometry. The main goal of the study is to review and systematize foreign studies related to the use of augmented reality in the process of learning geometry. All of them demonstrate the use of specially designed programs. The review consists of their analysis, the used equipment, purpose, capabilities, types of activities, types of markers, design and interface features, the content used and the degree of students' perception. The tasks and capabilities of the programs vary in difficulty levels and demonstrate the suitability of the technology for use in both primary and higher education. The above programs differ in design and ways of interacting with the interface. In particular, the introduction of the interface into the physical world, as noted by the authors of the relevant studies, creates a favorable impression, and gives the process a sensation that is different from ordinary work with a computer. During the analysis, it was determined that all applications were positively received by students, aroused interest, and increased willingness to learn. The use of augmented reality is possible for both individual and group work. There are successful examples of the use of technology in classroom and distance learning. Programs with augmented reality can serve as a successful didactic tool, making the training varied and interesting. application
{"title":"THE USE OF AUGMENTED REALITY IN THE STUDY OF GEOMETRY","authors":"K. Fomina","doi":"10.33842/2313-125X/2020/19/163/178","DOIUrl":"https://doi.org/10.33842/2313-125X/2020/19/163/178","url":null,"abstract":"The purpose of studying geometry is the development of spatial abilities. However, sometimes it is difficult for beginners to perceive two-dimensional images representing three-dimensional space in the learning process. Augmented reality is a technology that has demonstrated its effectiveness in learning and can be used to create didactic materials. Its feature is the placement of a virtual object in a real environment, in real-time and considering the location in space. Complementing the real environment with virtual information, it helps the user solve real-world problems. Despite the benefits, novelty, and interest in technology in the field of education, there are very few studies that demonstrate practical implementation and how to use it in the study of geometry. The main goal of the study is to review and systematize foreign studies related to the use of augmented reality in the process of learning geometry. All of them demonstrate the use of specially designed programs. The review consists of their analysis, the used equipment, purpose, capabilities, types of activities, types of markers, design and interface features, the content used and the degree of students' perception. The tasks and capabilities of the programs vary in difficulty levels and demonstrate the suitability of the technology for use in both primary and higher education. The above programs differ in design and ways of interacting with the interface. In particular, the introduction of the interface into the physical world, as noted by the authors of the relevant studies, creates a favorable impression, and gives the process a sensation that is different from ordinary work with a computer. During the analysis, it was determined that all applications were positively received by students, aroused interest, and increased willingness to learn. The use of augmented reality is possible for both individual and group work. There are successful examples of the use of technology in classroom and distance learning. Programs with augmented reality can serve as a successful didactic tool, making the training varied and interesting. application","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125754404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-08DOI: 10.33842/2313-125X/2020/19/65/69
S. Zalevsky, I. Pelevanuk
The paper considers one of the ways to construct geodetically parallel vectors on a curved surface. Solving this problem allows us to build a model of the Chebyshev grid on the surface. The model of the Chebyshev grid is called a mesh frame applied to the surface. It has the properties of this grid with a fairly short side length of the cell. The urgency of building a model of Chebyshev mesh on surfaces is due to the increasing use in mechanical engineering of fibrous composite materials that have a mesh structure. The property of the Chebyshev grid to remain Chebyshev with arbitrary bending can be used to construct a surface pattern of a complex technical form. The tangent vectors to the lines of one family of the Chebyshev grid drawn at their points of intersection with the lines of the second family are geodesically parallel. Therefore, the construction of such vectors along an arbitrary curve on the surface will allow to obtain a model of the Chebyshev grid in an arbitrarily chosen direction of the selected grid family. The method of geodesically parallel vector transfer along a given curve on the surface is proposed in the work. This curve is the line of stretching (throat) of the linear surface given by this family of directions. The proposed construction procedure allows for a relatively small number of calculations to obtain a vector field of the directions of the duck lines. Construction accuracy can be increased by reducing the linear construction parameter. Since the final result of the calculations is to create a model of the Chebyshev grid and obtain a pattern of mesh coating, the possibility of adjusting the construction parameters depending on the curvature of the surface is embedded in the code of the corresponding calculation program.
{"title":"GEODESICALLY PARALLEL TRANSFER OF A VECTOR ALONG THE CURVE ON THE SURFACE","authors":"S. Zalevsky, I. Pelevanuk","doi":"10.33842/2313-125X/2020/19/65/69","DOIUrl":"https://doi.org/10.33842/2313-125X/2020/19/65/69","url":null,"abstract":"The paper considers one of the ways to construct geodetically parallel vectors on a curved surface. Solving this problem allows us to build a model of the Chebyshev grid on the surface. The model of the Chebyshev grid is called a mesh frame applied to the surface. It has the properties of this grid with a fairly short side length of the cell. The urgency of building a model of Chebyshev mesh on surfaces is due to the increasing use in mechanical engineering of fibrous composite materials that have a mesh structure. The property of the Chebyshev grid to remain Chebyshev with arbitrary bending can be used to construct a surface pattern of a complex technical form. The tangent vectors to the lines of one family of the Chebyshev grid drawn at their points of intersection with the lines of the second family are geodesically parallel. Therefore, the construction of such vectors along an arbitrary curve on the surface will allow to obtain a model of the Chebyshev grid in an arbitrarily chosen direction of the selected grid family. The method of geodesically parallel vector transfer along a given curve on the surface is proposed in the work. This curve is the line of stretching (throat) of the linear surface given by this family of directions. The proposed construction procedure allows for a relatively small number of calculations to obtain a vector field of the directions of the duck lines. Construction accuracy can be increased by reducing the linear construction parameter. Since the final result of the calculations is to create a model of the Chebyshev grid and obtain a pattern of mesh coating, the possibility of adjusting the construction parameters depending on the curvature of the surface is embedded in the code of the corresponding calculation program.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115999575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-08DOI: 10.33842/2313-125X/2020/219/187/193
S. Shevchenko
Extinguishing fires in gas-liquid mixtures in vertical tanks containing flammable liquids should be accompanied by constant crushing of gas bubbles in these mixtures. The mechanical method makes it possible to crush the bubbles due to acoustic pressure waves generated by impacts on the metal membrane. A more progressive method of crushing involves the action of an acoustic wave directly on the bubbles. This allows you to intervene in the process of grinding the bubbles by changing the pressure frequency, which affects the quality of the gas-liquid mixture. In the works of Petrov A. and his students proposed a resonant model of grinding a gas bubble in a liquid in an unsteady pressure field. Resonant fragmentation of a bubble in a liquid occurs due to the transfer of energy between the radial and deformation modes of vibrations. An interesting effect is observed - with a relatively small amplitude of the alternating pressure of the acoustic wave in the liquid, a sufficiently large amplitude of deformation vibrations develops - due to which the bubble is crushed. A feature of research is the use for this mechanical analogue - a swinging spring (swinging spring). That is, a variety of a pendulum consisting of a point load attached to a weightless spring. The second end of the spring is fixed motionless. The pendulum oscillations of the spring in the vertical plane are studied, provided that its axis are straightforward. The feasibility of choosing such an analogue is explained by the need to study the dynamic system "grinding of the bubble" when nonlinearly coupled vibrational components exchange energy with each other. Indeed, in the case of a bubble, an energy exchange occurs between the radial and deformation modes of vibrations. In this paper, this phenomenon is investigated using the mathematical apparatus of a swinging spring, which illustrates the energy exchange between pendulum and spring oscillations.
在装有可燃液体的垂直罐中扑灭气液混合物中的火灾，应同时不断粉碎这些混合物中的气泡。机械方法通过冲击金属膜产生的声压波使气泡破碎成为可能。一种更渐进的破碎方法是声波直接作用于气泡。这样就可以通过改变压力频率来干预磨泡的过程，从而影响气液混合物的质量。在Petrov a .和他的学生的著作中，提出了在非定常压力场中在液体中研磨气泡的共振模型。液体中气泡的共振破碎是由于振动的径向和变形模式之间的能量传递而发生的。一个有趣的现象被观察到——在相对较小的声波在液体中的交变压力振幅下，产生了足够大的变形振动振幅——由于这种振动，气泡被压碎了。研究的一个特点是使用这种机械模拟物-摆动弹簧(摆动弹簧)。也就是说，一种由一个点载荷连接在一个失重弹簧上的钟摆。弹簧的第二端固定不动。研究了当弹簧的轴线为直线时，弹簧在垂直平面上的摆振。选择这种模拟的可行性是由于需要研究非线性耦合振动分量相互交换能量时的动态系统“磨泡”。事实上，在气泡的情况下，能量交换发生在振动的径向和变形模式之间。本文利用摆动弹簧的数学装置研究了这一现象，说明了摆振和弹簧振荡之间的能量交换。
{"title":"GAS BUBBLE CRUSHING MODELING BASED ON AN ANALOGY WITH A SWING SPRING","authors":"S. Shevchenko","doi":"10.33842/2313-125X/2020/219/187/193","DOIUrl":"https://doi.org/10.33842/2313-125X/2020/219/187/193","url":null,"abstract":"Extinguishing fires in gas-liquid mixtures in vertical tanks containing flammable liquids should be accompanied by constant crushing of gas bubbles in these mixtures. The mechanical method makes it possible to crush the bubbles due to acoustic pressure waves generated by impacts on the metal membrane. A more progressive method of crushing involves the action of an acoustic wave directly on the bubbles. This allows you to intervene in the process of grinding the bubbles by changing the pressure frequency, which affects the quality of the gas-liquid mixture. In the works of Petrov A. and his students proposed a resonant model of grinding a gas bubble in a liquid in an unsteady pressure field. Resonant fragmentation of a bubble in a liquid occurs due to the transfer of energy between the radial and deformation modes of vibrations. An interesting effect is observed - with a relatively small amplitude of the alternating pressure of the acoustic wave in the liquid, a sufficiently large amplitude of deformation vibrations develops - due to which the bubble is crushed. A feature of research is the use for this mechanical analogue - a swinging spring (swinging spring). That is, a variety of a pendulum consisting of a point load attached to a weightless spring. The second end of the spring is fixed motionless. The pendulum oscillations of the spring in the vertical plane are studied, provided that its axis are straightforward. The feasibility of choosing such an analogue is explained by the need to study the dynamic system \"grinding of the bubble\" when nonlinearly coupled vibrational components exchange energy with each other. Indeed, in the case of a bubble, an energy exchange occurs between the radial and deformation modes of vibrations. In this paper, this phenomenon is investigated using the mathematical apparatus of a swinging spring, which illustrates the energy exchange between pendulum and spring oscillations.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116960681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-08DOI: 10.33842/22195203/2020/19/11/16
I. Badayev, L. Lagodina
Relevance. Rational Bezier surfases and NURBS-surfases are widely used in modeling curviliniar objects due to the great flexibility and efficiency of the method. Therefore, it is sense to develop an interpolation method by these surfases Method. The work is devoted to the development of a new approach to interpolation surfases , represented by a set of discret points. The analytical description of the desired surfases is implemented a rational Bezier surfases and a NURBS-surfases.To solve this problem, two approaches are propozed. The first approach is that the weights of the control points are set in advance and then the coordinates of the points of the interpolating rational Bezier surfase as well as the NURBS-surfase are calculated. The second approach is that the coordinates of the control points are set in advance and then the weights of the control points of Bezier surfase as well as the NURBS-surfase are calculated. At the beginning of the process , are set only coordinates, but also parameters are set to a discret points, that is , each poins has the following definition: T(x,y,z,u,v) in the three-dimentional space, where u,v – parameters. To solve the interpolation problem, a system of linear equation is created in with each equation reflects the equality between the analytical formula for a surfase and a given point. Moreover, the number of interpolated points it must be number of control points. Thus, we have a system of N linear equations, where N is the number of control points. Results. Two methods of interpolation of a points serials by rational Bezier surfases and NURBS-surfases. were developed. Conclusions. The test cases carried out of using computer programs and calculated of results confirm the validiti of the proposed methods.
{"title":"INTERPOLATION BY RATIONAL SURFASES OF BEZIER AND NURBS-SURFASES","authors":"I. Badayev, L. Lagodina","doi":"10.33842/22195203/2020/19/11/16","DOIUrl":"https://doi.org/10.33842/22195203/2020/19/11/16","url":null,"abstract":"Relevance. Rational Bezier surfases and NURBS-surfases are widely used in modeling curviliniar objects due to the great flexibility and efficiency of the method. Therefore, it is sense to develop an interpolation method by these surfases Method. The work is devoted to the development of a new approach to interpolation surfases , represented by a set of discret points. The analytical description of the desired surfases is implemented a rational Bezier surfases and a NURBS-surfases.To solve this problem, two approaches are propozed. The first approach is that the weights of the control points are set in advance and then the coordinates of the points of the interpolating rational Bezier surfase as well as the NURBS-surfase are calculated. The second approach is that the coordinates of the control points are set in advance and then the weights of the control points of Bezier surfase as well as the NURBS-surfase are calculated. At the beginning of the process , are set only coordinates, but also parameters are set to a discret points, that is , each poins has the following definition: T(x,y,z,u,v) in the three-dimentional space, where u,v – parameters. To solve the interpolation problem, a system of linear equation is created in with each equation reflects the equality between the analytical formula for a surfase and a given point. Moreover, the number of interpolated points it must be number of control points. Thus, we have a system of N linear equations, where N is the number of control points. Results. Two methods of interpolation of a points serials by rational Bezier surfases and NURBS-surfases. were developed. Conclusions. The test cases carried out of using computer programs and calculated of results confirm the validiti of the proposed methods.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121775028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-08DOI: 10.33842/2313-125X/2020/19/124/129
A. Nesvidomina
The process of modeling the temperature distribution on surfaces, applying an image to curved areas with minimal distortion requires the formation of isometric grids on the plane and on the surface. One of the common ways to form planar isometric networks is to use the functions of a complex variable and planar isotropic curves, followed by separation of the real and imaginary parts. The development of computer models for the interactive search and analysis of isometric networks according to various initial geometric conditions provides a generalized method for their formation with the possibility of varying their shape and position. It is proposed to use an isotropic vector for the formation of flat isotropic curves, which ensured a single sequence of analytical calculations according to the following initial conditions: 1) selection of an arbitrary function of a real argument; 2) a given parametric equation of a plane curve; 3) a given polar equation of a plane curve. Since the analytical calculations of the derivation of the parametric equation of a plane isotropic curve and the corresponding isometric grid are rather laborious, their execution is carried out in the environment of the Maple symbolic algebra. To this end, the corresponding software has been created, which interactively allows you to select the function of a real argument, a parametric or polar equation of a plane guide curve. All subsequent stages of analytical transformations to form an isotropic curve and the corresponding isometric grid are carried out automatically. An interactive model for the formation and analysis of plane isotropic curves with various initial conditions has been created, which has shown its effectiveness, which is confirmed by the given examples of plane isometric grids for specific functions of the real parameter, plane curves in the parametric and polar form of their job.
{"title":"GENERALIZED METHOD FOR FORMING PLANE ISOTROPIC CURVES","authors":"A. Nesvidomina","doi":"10.33842/2313-125X/2020/19/124/129","DOIUrl":"https://doi.org/10.33842/2313-125X/2020/19/124/129","url":null,"abstract":"The process of modeling the temperature distribution on surfaces, applying an image to curved areas with minimal distortion requires the formation of isometric grids on the plane and on the surface. One of the common ways to form planar isometric networks is to use the functions of a complex variable and planar isotropic curves, followed by separation of the real and imaginary parts. The development of computer models for the interactive search and analysis of isometric networks according to various initial geometric conditions provides a generalized method for their formation with the possibility of varying their shape and position. It is proposed to use an isotropic vector for the formation of flat isotropic curves, which ensured a single sequence of analytical calculations according to the following initial conditions: 1) selection of an arbitrary function of a real argument; 2) a given parametric equation of a plane curve; 3) a given polar equation of a plane curve. Since the analytical calculations of the derivation of the parametric equation of a plane isotropic curve and the corresponding isometric grid are rather laborious, their execution is carried out in the environment of the Maple symbolic algebra. To this end, the corresponding software has been created, which interactively allows you to select the function of a real argument, a parametric or polar equation of a plane guide curve. All subsequent stages of analytical transformations to form an isotropic curve and the corresponding isometric grid are carried out automatically. An interactive model for the formation and analysis of plane isotropic curves with various initial conditions has been created, which has shown its effectiveness, which is confirmed by the given examples of plane isometric grids for specific functions of the real parameter, plane curves in the parametric and polar form of their job.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"21 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120859676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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