The goal of this article is to develop a generalized mathematical model for controlling the motion of the spacecraft of a space industrial platform’s distributed power system. Space industrialization is one of the promising lines of industrial development in the world. The development of space industrial technologies will allow one to solve a number of problems in the production of unique products unavailable under terrestrial conditions. The main types of these products include semiconductor materials, materials made by 3D printing in microgravity, space modules of sunshade systems, space metallurgy products, space debris processing products, and high-purity space biology substances. Taking this into account, a certain amount of electricity is required for the manufacture of one or another product. Given that some space industrial processes can consume a significant amount of electricity, a space industrial platform's own power generation may not be sufficient. Because of this, it was proposed to use additional energy resources through the development of a distributed power supply system for a space industrial platform. A group of power spacecraft is envisaged to collect and accumulate electric energy and transmit it in a contactless way to the receivers of the space industrial platform. The article presents mathematical models for the analysis of the orbital, angular, and relative motion of power spacecraft and receiver spacecraft. Algorithms are proposed for calculating the parameters of the power spacecraft orientation and stabilization system. A generalized model is constructed for determining the maximum distance and time interval of power spacecraft to platform electric power transmission using microwave radiation. The model developed allows one to choose the power spacecraft design parameters at the stage of conceptual design of space industrial platform power systems.
{"title":"Model of distributed space power system motion control","authors":"O. Palii, E. Lapkhanov, D. Svorobin","doi":"10.15407/itm2022.04.035","DOIUrl":"https://doi.org/10.15407/itm2022.04.035","url":null,"abstract":"The goal of this article is to develop a generalized mathematical model for controlling the motion of the spacecraft of a space industrial platform’s distributed power system. Space industrialization is one of the promising lines of industrial development in the world. The development of space industrial technologies will allow one to solve a number of problems in the production of unique products unavailable under terrestrial conditions. The main types of these products include semiconductor materials, materials made by 3D printing in microgravity, space modules of sunshade systems, space metallurgy products, space debris processing products, and high-purity space biology substances. Taking this into account, a certain amount of electricity is required for the manufacture of one or another product. Given that some space industrial processes can consume a significant amount of electricity, a space industrial platform's own power generation may not be sufficient. Because of this, it was proposed to use additional energy resources through the development of a distributed power supply system for a space industrial platform. A group of power spacecraft is envisaged to collect and accumulate electric energy and transmit it in a contactless way to the receivers of the space industrial platform. The article presents mathematical models for the analysis of the orbital, angular, and relative motion of power spacecraft and receiver spacecraft. Algorithms are proposed for calculating the parameters of the power spacecraft orientation and stabilization system. A generalized model is constructed for determining the maximum distance and time interval of power spacecraft to platform electric power transmission using microwave radiation. The model developed allows one to choose the power spacecraft design parameters at the stage of conceptual design of space industrial platform power systems.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130613148","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}
The aim of this work is to develop a procedure for determining the ion dissociation degree and the electron density in a supersonic jet of a gas-discharge source of collisionless plasma from the results of measurements of the current collected by an insulated probe system with transversely oriented cylindrical electrodes. Based on a mathematical model of current collection by an insulated probe system and an asymptotic solution for the probe current in the electron saturation region obtained previously, new computational formulas for plasma parameter determination are derived. It is shown that, in comparison with a single Langmuir probe, an insulated probe system provides more information in diagnosing a jet of a gas-discharge source of laboratory plasma. The effect of the probe to reference electrode current collection area ratio and the probe measurement errors on the plasma parameter determination accuracy is studied numerically. Within the framework of the mathematical model of current collection, an analysis is made of the effect of the geometrical parameters of the insulated probe system on the method error in plasma parameter determination using the asymptotic solution for the probe current in the electron saturation region. For the determination of the ion dissociation degree, optimal values of the insulated probe system’s bias potentials and geometrical parameters (probe to reference electrode area ratio) are found. For the adopted assumptions, the reliability of ion dissociation degree and electron density determination is estimated as a function of the geometrical parameters of the insulated probe system and the probe current and probe potential (relative to the reference electrode) measurement accuracy. The obtained results may be used in the diagnostics of the laboratory plasma of a gas-discharge source with ion acceleration in the electric field of the jet.
{"title":"Determination of plasma parameters in a jet of a gas-discharge source using an insulated probe system with cylindrical electrodes","authors":"D. Lazuchenkov","doi":"10.15407/itm2022.04.121","DOIUrl":"https://doi.org/10.15407/itm2022.04.121","url":null,"abstract":"The aim of this work is to develop a procedure for determining the ion dissociation degree and the electron density in a supersonic jet of a gas-discharge source of collisionless plasma from the results of measurements of the current collected by an insulated probe system with transversely oriented cylindrical electrodes. Based on a mathematical model of current collection by an insulated probe system and an asymptotic solution for the probe current in the electron saturation region obtained previously, new computational formulas for plasma parameter determination are derived. It is shown that, in comparison with a single Langmuir probe, an insulated probe system provides more information in diagnosing a jet of a gas-discharge source of laboratory plasma. The effect of the probe to reference electrode current collection area ratio and the probe measurement errors on the plasma parameter determination accuracy is studied numerically. Within the framework of the mathematical model of current collection, an analysis is made of the effect of the geometrical parameters of the insulated probe system on the method error in plasma parameter determination using the asymptotic solution for the probe current in the electron saturation region. For the determination of the ion dissociation degree, optimal values of the insulated probe system’s bias potentials and geometrical parameters (probe to reference electrode area ratio) are found. For the adopted assumptions, the reliability of ion dissociation degree and electron density determination is estimated as a function of the geometrical parameters of the insulated probe system and the probe current and probe potential (relative to the reference electrode) measurement accuracy. The obtained results may be used in the diagnostics of the laboratory plasma of a gas-discharge source with ion acceleration in the electric field of the jet.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133022635","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}
When solving parametric reliability problems, one often has to construct distributions of statistical data to find the probability of containment in the operability region. This paper considers the problem of 2D statistical ensemble fitting. The use of a 2D normal distribution in statistical data description is not always justified because statistical ensembles rather frequently (at the level of marginal components and a stochastic relationship between them) have properties different from the normal case. From a practical standpoint, it is desirable for researchers to describe 2D statistical ensembles with the use of universal distributions, which allow one to cover a wide range of source data using a single analytical form. In the process of fitting, account should be made of bounded ranges of random variables. The paper considers who universal distribution construction methods, which are based on 1D orthogonal Jacobi polynomial expansions. In these distributions, the random variable range is a rectangle. In the first method, a 2D distribution is constructed using a direct expansion in the 1D Jacobi polynomials. A 2D Jacobi distribution function and regression lines are obtained, and methods to fit it are considered. In theory, a distribution obtained in this way can be used, up to the fourth order inclusive, for marginal and even reduced moments different from the normal case. However, its real capabilities are limited to values of reduced moments (1D and even) that differ from the normal case only very slightly. Otherwise, the probability surface may enter negative ranges with the occurrence of multiple modes. The second way to construct a 2D distribution is to use a normal copula and 1D Jacobi distributions as components. The resulting 2D distribution allows one to deal with 1D distributions different from the normal case and linear correlation. This approach is justified because, according to research data, it is a linear stochastic relationship that relates a significant part of 2D statistical ensembles, and marginal distributions deviate from the normal case. Regression lines of a distribution of this kind are obtained, and it is shown that they are curved because marginal distributions differ from the normal one. The paper considers the practical example of fitting a 2D ensemble of characteristics of a liquid-propellant rocket engine some components of which are related via a linear stochastic relationship (the parameters that characterize a nonlinear stochastic relationship proved to be insignificant) and have 1D distributions different from the normal one. The fitted and observed frequencies are in rather good agreement. It is shown that a distribution based on a normal copula is more universal, and it is recommended for practical calculations.
{"title":"Construction and analysis of universal 2D distributions with a bounded rectangular variation domain","authors":"E. Hladkyi, V.I. Perlyk","doi":"10.15407/itm2022.04.095","DOIUrl":"https://doi.org/10.15407/itm2022.04.095","url":null,"abstract":"When solving parametric reliability problems, one often has to construct distributions of statistical data to find the probability of containment in the operability region. This paper considers the problem of 2D statistical ensemble fitting. The use of a 2D normal distribution in statistical data description is not always justified because statistical ensembles rather frequently (at the level of marginal components and a stochastic relationship between them) have properties different from the normal case. From a practical standpoint, it is desirable for researchers to describe 2D statistical ensembles with the use of universal distributions, which allow one to cover a wide range of source data using a single analytical form. In the process of fitting, account should be made of bounded ranges of random variables. The paper considers who universal distribution construction methods, which are based on 1D orthogonal Jacobi polynomial expansions. In these distributions, the random variable range is a rectangle. In the first method, a 2D distribution is constructed using a direct expansion in the 1D Jacobi polynomials. A 2D Jacobi distribution function and regression lines are obtained, and methods to fit it are considered. In theory, a distribution obtained in this way can be used, up to the fourth order inclusive, for marginal and even reduced moments different from the normal case. However, its real capabilities are limited to values of reduced moments (1D and even) that differ from the normal case only very slightly. Otherwise, the probability surface may enter negative ranges with the occurrence of multiple modes. The second way to construct a 2D distribution is to use a normal copula and 1D Jacobi distributions as components. The resulting 2D distribution allows one to deal with 1D distributions different from the normal case and linear correlation. This approach is justified because, according to research data, it is a linear stochastic relationship that relates a significant part of 2D statistical ensembles, and marginal distributions deviate from the normal case. Regression lines of a distribution of this kind are obtained, and it is shown that they are curved because marginal distributions differ from the normal one. The paper considers the practical example of fitting a 2D ensemble of characteristics of a liquid-propellant rocket engine some components of which are related via a linear stochastic relationship (the parameters that characterize a nonlinear stochastic relationship proved to be insignificant) and have 1D distributions different from the normal one. The fitted and observed frequencies are in rather good agreement. It is shown that a distribution based on a normal copula is more universal, and it is recommended for practical calculations.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130032090","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}
The goal of this work is to develop a methodological approach to quantitative estimation of the risk of an increase in the cost of space hardware prototyping. The paper considers a technology and mathematical models for quantitative estimation of the risk of an increase in the cost of a developmental work on space hardware prototyping. The main cause of the risk of development cost increase is that data used in expected cost estimation are incomplete and inaccurate. The risk level is estimated as the probability of the possible cost of an R&D project exceeding a critical (for the investor) value. The risk estimation technology is constructed on the basis of the Monte Carlo method embedded in a simulation model. The Monte Carlo method is based on an analytico-probabilistic model (a deterministic mathematical model and a probabilistic model with known distribution functions (laws)). The uniqueness, novelty, and technical complexity of space hardware prototypes do not allow one to construct any analytico-probabilistic model. This paper presents a mathematical model equivalent to an analytico-probabilistic one. The paper substantiates the appropriateness of a homomorphic mapping of a possibilistic space of random variables into a probabilistic space; i.e. in this case the proposed model is equivalent to an analytico-probabilistic one. The key component of the simulation model is the mathematical model of the development cost of a space hardware prototype. The cost model is based on a component-by-component analogy for relatively simple components of the space hardware prototype, moving (upward) along the weighted oriented tree graph that models the engineering structure of the space hardware prototype, and fuzzy methods. The proposed methodological approach may be used in the construction of a simulation model for quantitative estimation vc of the risk of a decrease in the efficiency of use of the prototype under development. To do this, it will be sufficient to replace the mathematical model of development cost with a mathematical model of expected efficiency.
{"title":"Quantitative estimation of the risk of an increase in the cost of space hardware prototyping","authors":"A. Alpatov, V. T. Marchenko, N. Sazina","doi":"10.15407/itm2022.04.051","DOIUrl":"https://doi.org/10.15407/itm2022.04.051","url":null,"abstract":"The goal of this work is to develop a methodological approach to quantitative estimation of the risk of an increase in the cost of space hardware prototyping. The paper considers a technology and mathematical models for quantitative estimation of the risk of an increase in the cost of a developmental work on space hardware prototyping. The main cause of the risk of development cost increase is that data used in expected cost estimation are incomplete and inaccurate. The risk level is estimated as the probability of the possible cost of an R&D project exceeding a critical (for the investor) value. The risk estimation technology is constructed on the basis of the Monte Carlo method embedded in a simulation model. The Monte Carlo method is based on an analytico-probabilistic model (a deterministic mathematical model and a probabilistic model with known distribution functions (laws)). The uniqueness, novelty, and technical complexity of space hardware prototypes do not allow one to construct any analytico-probabilistic model. This paper presents a mathematical model equivalent to an analytico-probabilistic one. The paper substantiates the appropriateness of a homomorphic mapping of a possibilistic space of random variables into a probabilistic space; i.e. in this case the proposed model is equivalent to an analytico-probabilistic one. The key component of the simulation model is the mathematical model of the development cost of a space hardware prototype. The cost model is based on a component-by-component analogy for relatively simple components of the space hardware prototype, moving (upward) along the weighted oriented tree graph that models the engineering structure of the space hardware prototype, and fuzzy methods. The proposed methodological approach may be used in the construction of a simulation model for quantitative estimation vc of the risk of a decrease in the efficiency of use of the prototype under development. To do this, it will be sufficient to replace the mathematical model of development cost with a mathematical model of expected efficiency.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114547946","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}
The relevance of this work stems from the urgent need for the modern development of the Ukrainian railway transport and the acceleration of Ukraine's integration into the European railway transportation. Currently, the most effective way to travel across borders between countries with different track gauges is the use of gauge-changeable wheelsets, a system that can change from one gauge to another when moving through special gauge changing facilities. The use of cars with gauge-changeable wheelsets on the Ukrainian and European railways calls for assuring a good compatibility of the wheel-rail pair on tracks of both gauges. The goal of this work was to develop a unified wheel profile for the operation on the domestic and European railways and predict the safety of cars with that wheel profile, the ride quality, and processes of wheel-rail dynamic interaction for tracks with different parameters. Use was made of methods of deformable solid mechanics, statistical dynamics, and numerical integration. A family of wheel profiles was constructed, and the effectiveness of their use in passenger car wheelsets on the Ukrainian (1520 mm gauge) and European (1435 mm gauge) railways was evaluated. For each profile, the spatial problem of wheel?rail contact was solved, and the interaction parameters were analyzed, including the dimensions and location of the contact patches. Calculations were also made for a car negotiating a circular curve of a small radius (R = 300 m) and moving at different speeds on tangent track sections. The choice among the constructed profiles was made according to two criteria: wheel flange wear and car dynamic stability. Based on the studies conducted, a new wear-resistant wheel profile, ITM-73EP, was proposed. Its use in gauge-changeable wheelsets of passenger cars will provide reasonable indices of wheel–rail interaction both on the Ukrainian and on the European railways without sacrificing car dynamic performance.
{"title":"Passenger car wheel profile for the operation on the Ukrainian and European railways","authors":"T. Mokrii, I. Malysheva, L. Lapina, N. Bezrukavyi","doi":"10.15407/itm2022.04.111","DOIUrl":"https://doi.org/10.15407/itm2022.04.111","url":null,"abstract":"The relevance of this work stems from the urgent need for the modern development of the Ukrainian railway transport and the acceleration of Ukraine's integration into the European railway transportation. Currently, the most effective way to travel across borders between countries with different track gauges is the use of gauge-changeable wheelsets, a system that can change from one gauge to another when moving through special gauge changing facilities. The use of cars with gauge-changeable wheelsets on the Ukrainian and European railways calls for assuring a good compatibility of the wheel-rail pair on tracks of both gauges. The goal of this work was to develop a unified wheel profile for the operation on the domestic and European railways and predict the safety of cars with that wheel profile, the ride quality, and processes of wheel-rail dynamic interaction for tracks with different parameters. Use was made of methods of deformable solid mechanics, statistical dynamics, and numerical integration. A family of wheel profiles was constructed, and the effectiveness of their use in passenger car wheelsets on the Ukrainian (1520 mm gauge) and European (1435 mm gauge) railways was evaluated. For each profile, the spatial problem of wheel?rail contact was solved, and the interaction parameters were analyzed, including the dimensions and location of the contact patches. Calculations were also made for a car negotiating a circular curve of a small radius (R = 300 m) and moving at different speeds on tangent track sections. The choice among the constructed profiles was made according to two criteria: wheel flange wear and car dynamic stability. Based on the studies conducted, a new wear-resistant wheel profile, ITM-73EP, was proposed. Its use in gauge-changeable wheelsets of passenger cars will provide reasonable indices of wheel–rail interaction both on the Ukrainian and on the European railways without sacrificing car dynamic performance.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126796767","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}
O. Pylypenko, O. Nikolayev, I. D. Bashliy, O. Zavoloka
Space propulsion systems ensure multiple startups and shutdowns of the main liquid-propellant rocket engines in microgravity conditions for spacecraft preset motions and reorientation control. During the passive flight of a space stage (after its main engine shutdown), the liquid propellant in the tanks continues moving by inertia in microgravity and moves as far away from the propellant management device as possible. In this case, the pressurization gas is displaced to the propellant management device, which creates the potential danger of the gas entering the engine inlet in quantities unacceptable for multiple reliable engine restarts. In this regard, the determination of the parameters of fluid movement in propellant tanks under microgravity conditions is a pertinent problem to be solved in the designing of liquid-propellant propulsion systems. This paper presents an approach to the theoretical calculation of the parameters of motion of the gas–liquid system in the propellant tanks of today’s space stages in microgravity conditions. The approach is based on the use of the finite element method, the Volume of Fluid method, and up-to-date computer tools for finite-element analysis (Computer Aided Engineering - CAE systems). A mathematical simulation of the spatial motion of the liquid propellant and the formation of free gas inclusions in passive flight was performed, and the motion parameters and shape of the free liquid surface in the tank and the location of gas inclusions were determined. The liquid motion in a model spherical tank in microgravity conditions was simulated numerically with and without account for the hot zone near the tank head. The motion parameters of the gas-liquid interface in a model cylindrical tank found using the proposed approach are in satisfactory agreement with experimental data. The proposed approach will significantly reduce the extent of experimental testing of space stages under development.
{"title":"Approach to numerical simulation of the spatial motions of a gas/liquid medium in a space stage propellant tank in microgravity with account for the hot zone","authors":"O. Pylypenko, O. Nikolayev, I. D. Bashliy, O. Zavoloka","doi":"10.15407/itm2022.04.003","DOIUrl":"https://doi.org/10.15407/itm2022.04.003","url":null,"abstract":"Space propulsion systems ensure multiple startups and shutdowns of the main liquid-propellant rocket engines in microgravity conditions for spacecraft preset motions and reorientation control. During the passive flight of a space stage (after its main engine shutdown), the liquid propellant in the tanks continues moving by inertia in microgravity and moves as far away from the propellant management device as possible. In this case, the pressurization gas is displaced to the propellant management device, which creates the potential danger of the gas entering the engine inlet in quantities unacceptable for multiple reliable engine restarts. In this regard, the determination of the parameters of fluid movement in propellant tanks under microgravity conditions is a pertinent problem to be solved in the designing of liquid-propellant propulsion systems. This paper presents an approach to the theoretical calculation of the parameters of motion of the gas–liquid system in the propellant tanks of today’s space stages in microgravity conditions. The approach is based on the use of the finite element method, the Volume of Fluid method, and up-to-date computer tools for finite-element analysis (Computer Aided Engineering - CAE systems). A mathematical simulation of the spatial motion of the liquid propellant and the formation of free gas inclusions in passive flight was performed, and the motion parameters and shape of the free liquid surface in the tank and the location of gas inclusions were determined. The liquid motion in a model spherical tank in microgravity conditions was simulated numerically with and without account for the hot zone near the tank head. The motion parameters of the gas-liquid interface in a model cylindrical tank found using the proposed approach are in satisfactory agreement with experimental data. The proposed approach will significantly reduce the extent of experimental testing of space stages under development.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"378 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133168159","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}
This paper presents a mathematical model of vibrations of a three-layered double-curved shell under geometrically nonlinear deformation. The middle layer is a honeycomb manufactured using FDM additive technologies. The mechanical properties of the honeycomb were assessed by a homogenization procedure. The outer layers of the shell are thin, and they are made of carbon-filled plastic. The model is based on a higher-order shear theory and accounts for the orthotropy of the mechanical properties of all the shell layers. Each layer of the shell is described by five variables (three displacement projections and two rotation angles of the normal to the middle surface). The properties of linear vibrations were studied using discretization by the Rayleigh?Ritz method. Because the middle layer of the shell is far lighter and more compliant in comparison with the outer layers, the computational process has some features. The eigenferquencies and eigenmodes of the shell were found for a further analysis of nonlinear vibrations. The mathematical model of forced vibrations of the shell under geometrically nonlinear deformation is a system of nonlinear ordinary differential equations derived by the assumed-mode method. Nonlinear periodic vibrations and their bifurcations were studied using a numerical procedure, which is a combination of the continuation method and the shooting technique. The properties of the nonlinear periodic vibrations and their bifurcations in the regions of fundamental and subharmonic resonances were studied numerically. A spherical panel and a hyperbolic paraboloid panel were considered. It was shown that when a disturbing force is applied at a point out of the panel’s center of gravity, the panel’s eigenmodes interact, and the frequency response and the bifurcation diagram change qualitatively in comparison with the case where that force is applied at the panel’s center of gravity. An agreement between the results was studied as a function of the number of terms in the Rayleigh-Ritz and assumed-mode expansions.
{"title":"Forced vibrations of a three-layered double-curved shell with an elastic honeycomb core","authors":"K. Avramov, B. Uspensky","doi":"10.15407/itm2022.04.079","DOIUrl":"https://doi.org/10.15407/itm2022.04.079","url":null,"abstract":"This paper presents a mathematical model of vibrations of a three-layered double-curved shell under geometrically nonlinear deformation. The middle layer is a honeycomb manufactured using FDM additive technologies. The mechanical properties of the honeycomb were assessed by a homogenization procedure. The outer layers of the shell are thin, and they are made of carbon-filled plastic. The model is based on a higher-order shear theory and accounts for the orthotropy of the mechanical properties of all the shell layers. Each layer of the shell is described by five variables (three displacement projections and two rotation angles of the normal to the middle surface). The properties of linear vibrations were studied using discretization by the Rayleigh?Ritz method. Because the middle layer of the shell is far lighter and more compliant in comparison with the outer layers, the computational process has some features. The eigenferquencies and eigenmodes of the shell were found for a further analysis of nonlinear vibrations. The mathematical model of forced vibrations of the shell under geometrically nonlinear deformation is a system of nonlinear ordinary differential equations derived by the assumed-mode method. Nonlinear periodic vibrations and their bifurcations were studied using a numerical procedure, which is a combination of the continuation method and the shooting technique. The properties of the nonlinear periodic vibrations and their bifurcations in the regions of fundamental and subharmonic resonances were studied numerically. A spherical panel and a hyperbolic paraboloid panel were considered. It was shown that when a disturbing force is applied at a point out of the panel’s center of gravity, the panel’s eigenmodes interact, and the frequency response and the bifurcation diagram change qualitatively in comparison with the case where that force is applied at the panel’s center of gravity. An agreement between the results was studied as a function of the number of terms in the Rayleigh-Ritz and assumed-mode expansions.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131866641","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}
S. Khoroshylov, V.K. Shamakhanov, S.E. Martyniuk, O. Sushko
The goal of this article is to develop a dynamic model of a space antenna with the pantograph structure and to study the processes of its deployment using open-source software. Methods of theoretical mechanics, multibody dynamics, computational mechanics, and computer modeling were used in the research. A mesh antenna of the novel design, which is recommended for mini-satellites, is considered as the object for modeling. The most significant difference between this antenna and others is the design of the support ring in the form of a pantograph. To develop a model of the space antenna dynamics and implement it using open-source software, some simplifications were made due to the complexity of the structure. The antenna model is represented as a system of rigid and flexible bodies connected by hinges. Carbon fiber rods are modeled with the help of a flexible finite element using the method of absolute nodal coordinates, which allows one to model large deformations of the structure. Aluminum hinge assemblies are modeled as several rotation joints connected by conventional rigid elements. The main modeled properties of these hinge assemblies are the stiffness, location, and direction of the axes of rotation of the hinges. The tension forces created by the stretched mesh are modeled using springs. The cable drive of the antenna deployment mechanism is modeled as a load acting on the corresponding elements in defined local positions. An algorithm for building a model of the space antenna to simulate the reflector deployment process in the HotInt open-source software is presented. Using the built model, antenna deployment simulations are carried out for different cases, which differ in the forces used for the deployment. Values of deployment time, variations of angles between the V-folded bars, and tensions in the diagonal rods of the antenna sections during the antenna deployment are obtained. The approach proposed in the article can be implemented using free software, ensures flexibility of modeling, and reduces the model development time.
{"title":"Modelling of space antenna deployment using open source software","authors":"S. Khoroshylov, V.K. Shamakhanov, S.E. Martyniuk, O. Sushko","doi":"10.15407/itm2022.04.014","DOIUrl":"https://doi.org/10.15407/itm2022.04.014","url":null,"abstract":"The goal of this article is to develop a dynamic model of a space antenna with the pantograph structure and to study the processes of its deployment using open-source software. Methods of theoretical mechanics, multibody dynamics, computational mechanics, and computer modeling were used in the research. A mesh antenna of the novel design, which is recommended for mini-satellites, is considered as the object for modeling. The most significant difference between this antenna and others is the design of the support ring in the form of a pantograph. To develop a model of the space antenna dynamics and implement it using open-source software, some simplifications were made due to the complexity of the structure. The antenna model is represented as a system of rigid and flexible bodies connected by hinges. Carbon fiber rods are modeled with the help of a flexible finite element using the method of absolute nodal coordinates, which allows one to model large deformations of the structure. Aluminum hinge assemblies are modeled as several rotation joints connected by conventional rigid elements. The main modeled properties of these hinge assemblies are the stiffness, location, and direction of the axes of rotation of the hinges. The tension forces created by the stretched mesh are modeled using springs. The cable drive of the antenna deployment mechanism is modeled as a load acting on the corresponding elements in defined local positions. An algorithm for building a model of the space antenna to simulate the reflector deployment process in the HotInt open-source software is presented. Using the built model, antenna deployment simulations are carried out for different cases, which differ in the forces used for the deployment. Values of deployment time, variations of angles between the V-folded bars, and tensions in the diagonal rods of the antenna sections during the antenna deployment are obtained. The approach proposed in the article can be implemented using free software, ensures flexibility of modeling, and reduces the model development time.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133844200","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}
This work is aimed at determining the expediency of using a nanofliud (a special suspension with nanoparticles) as a heat transfer agent for a parabolic trough solar plant. Adding nanoparticles to a base heat transfer agent intensifies convective heat exchange inside the channel, thus increasing the total heat efficiency of the receiver system. A refined nonlinear 3D mathematical model was developed to study heat-and-mass transfer in the receiver system of a parabolic trough solar plant that consist of a concentrator and a tube heat receiver with a nanofluid. In the mathematical model, the values of the nonuniform heat flux on the tube heat receiver surface are found by approximating numerical data obtained by the Monte Carlo method. This simplifies the classical coupled deterministic-statistical mathematical model and allows one to obtain a purely deterministic model solved by the finite volume method. The model also accounts for the thermal conductivity of the heat receiver wall, the actual ambient conditions, and the heat loss from the heat receiver surface. A numerical algorithm was developed to conduct numerical parametric studies on determining the temperature fields of Syltherm800/Al2O3 nanofluid heat transfer agent. This nanofluid is prepared from the traditional heat transfer agent of parabolic trough solar plants – Syltherm800 silicone oil – by adding aluminum oxide nanoparticles thereto. The numerical studies were conducted both for pure Syltherm800 oil and for Syltherm800/Al2O3 nanofluid with an Al2O3 nanoparticle concentration of 3, 5, and 8 per cent. This study is the first to find that the use of a nanofluid as a heat transfer agent for a parabolic trough solar plant produces a positive effect only in the case of the laminar flow of a nanofluid heat transfer agent with a high nanoparticle concentration. A verification of the obtained numerical data showed that they are in satisfactory agreement with experimental ones.
{"title":"Mathematical model of heat mass exchange in a channel with a nanofluid un-der nonuniform heating by a concentrated heat flux","authors":"A. Borysenko, L. Knysh","doi":"10.15407/itm2022.03.099","DOIUrl":"https://doi.org/10.15407/itm2022.03.099","url":null,"abstract":"This work is aimed at determining the expediency of using a nanofliud (a special suspension with nanoparticles) as a heat transfer agent for a parabolic trough solar plant. Adding nanoparticles to a base heat transfer agent intensifies convective heat exchange inside the channel, thus increasing the total heat efficiency of the receiver system. A refined nonlinear 3D mathematical model was developed to study heat-and-mass transfer in the receiver system of a parabolic trough solar plant that consist of a concentrator and a tube heat receiver with a nanofluid. In the mathematical model, the values of the nonuniform heat flux on the tube heat receiver surface are found by approximating numerical data obtained by the Monte Carlo method. This simplifies the classical coupled deterministic-statistical mathematical model and allows one to obtain a purely deterministic model solved by the finite volume method. The model also accounts for the thermal conductivity of the heat receiver wall, the actual ambient conditions, and the heat loss from the heat receiver surface. A numerical algorithm was developed to conduct numerical parametric studies on determining the temperature fields of Syltherm800/Al2O3 nanofluid heat transfer agent. This nanofluid is prepared from the traditional heat transfer agent of parabolic trough solar plants – Syltherm800 silicone oil – by adding aluminum oxide nanoparticles thereto. The numerical studies were conducted both for pure Syltherm800 oil and for Syltherm800/Al2O3 nanofluid with an Al2O3 nanoparticle concentration of 3, 5, and 8 per cent. This study is the first to find that the use of a nanofluid as a heat transfer agent for a parabolic trough solar plant produces a positive effect only in the case of the laminar flow of a nanofluid heat transfer agent with a high nanoparticle concentration. A verification of the obtained numerical data showed that they are in satisfactory agreement with experimental ones.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125458968","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}
The diagnostics of low-temperature plasma flows using cylindrical probes is based on the classical Langmuir relation for the ion current to a thin, in comparison with the Debye length, cylinder. The aim of this work is to study the applicability of the Langmuir relation for a cylinder whose radius exceeds the Debye length. The interaction of a conducting cylinder with a rarefied plasma flow was simulated numerically. The cylinder had a negative potential with respect to the plasma. Free molecular flow around the cylinder was simulated on the basis of a two-dimensional system of the Vlasov–Poisson equations. The electron-repulsing local equilibrium self-consistent electric field was calculated using the Poisson–Boltzmann model in the approximation of local equilibrium electrons and taking into account an electron sink on the cylinder surface in the central field approximation. The Vlasov equations for ions and the Poisson–Boltzmann equations for the self-consistent electric field were solved on nested grids by a finite-difference relaxation method with splitting by physical processes and using the method of characteristics. The reliability of the calculated results was confirmed by the solution of known model problems and a comparison with the results of other authors and the results of solving identical physical problems with the use of different mathematical models and methods. The ion current to a cylinder placed transversely to a plasma flow was calculated as a function of the cylinder potential, the ion velocity ratio, and the ratio of the characteristic dimension of the cylinder to the Debye length. From the calculated results, numerical estimates were obtained for the range of applicability of the classical Langmuir relation for the ion current to a cylinder whose radius exceeds the Debye length. The results obtained may be used in the diagnostics of supersonic flows of a low-temperature rarefied plasma.
{"title":"Calculation of the ion current to a conducting cylinder in a supersonic flow of a collisionless plasma","authors":"D. Lazuchenkov, N. Lazuchenkov","doi":"10.15407/itm2022.03.091","DOIUrl":"https://doi.org/10.15407/itm2022.03.091","url":null,"abstract":"The diagnostics of low-temperature plasma flows using cylindrical probes is based on the classical Langmuir relation for the ion current to a thin, in comparison with the Debye length, cylinder. The aim of this work is to study the applicability of the Langmuir relation for a cylinder whose radius exceeds the Debye length. The interaction of a conducting cylinder with a rarefied plasma flow was simulated numerically. The cylinder had a negative potential with respect to the plasma. Free molecular flow around the cylinder was simulated on the basis of a two-dimensional system of the Vlasov–Poisson equations. The electron-repulsing local equilibrium self-consistent electric field was calculated using the Poisson–Boltzmann model in the approximation of local equilibrium electrons and taking into account an electron sink on the cylinder surface in the central field approximation. The Vlasov equations for ions and the Poisson–Boltzmann equations for the self-consistent electric field were solved on nested grids by a finite-difference relaxation method with splitting by physical processes and using the method of characteristics. The reliability of the calculated results was confirmed by the solution of known model problems and a comparison with the results of other authors and the results of solving identical physical problems with the use of different mathematical models and methods. The ion current to a cylinder placed transversely to a plasma flow was calculated as a function of the cylinder potential, the ion velocity ratio, and the ratio of the characteristic dimension of the cylinder to the Debye length. From the calculated results, numerical estimates were obtained for the range of applicability of the classical Langmuir relation for the ion current to a cylinder whose radius exceeds the Debye length. The results obtained may be used in the diagnostics of supersonic flows of a low-temperature rarefied plasma.","PeriodicalId":287730,"journal":{"name":"Technical mechanics","volume":"39 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128775935","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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