{"title":"BIFURCATIONS OF STATIONARY REGIMES IN THE MODEL OF A WIND POWER PLANT","authors":"A. S. Kirsanova","doi":"10.18287/2541-7525-2021-27-4-92-98","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-4-92-98","url":null,"abstract":"The article should use a mathematical model of a wind power plant. In the chosen world, alternative energy is actively developing, as natural resources for harmful energy carriers are significantly reduced every year. In turn, the energy reserves of life situations turned out to be related to world problems. Thus, the relevance of this problem is solved in the free system of the wind section. The complexity of this work is determined by the fact that the model, which is not defined, is found completely, that is, part of the functions in the mathematical model is setonly graphically, based on experimental data. The graph of relative aerodynamic moment of forces is approximated. The ratio of stationary modes is studied for various values of external resistance of the dynamic model. Conditions are found under which a saddle-node bifurcation and a supercritical AndronovHopf bifurcation are observed in the system.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125096771","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}
{"title":"COMPARATIVE ANALYSIS OF STRESS STATE IN THE VICINITY OF THE CRACK-TIPS AND NOTCHES USING TRUNCATED WILLIAMS SERIES EXPANSION","authors":"R. M. Zhabbarov, L. Stepanova","doi":"10.18287/2541-7525-2021-27-4-30-67","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-4-30-67","url":null,"abstract":"In the present study the asymptotic analysis of the multi-parameter Williams series expansion of the stress-strain state in the vicinity of seven different configurations is performed. The aim of the asymptotic analysis is to educate the sensitivity of different cracked and notched configurations to the number of kept terms in Williams series expansion. It is shown that all configurations with the concentrated forces possess the more sensitivity to the number of terms in the truncated Williams series expansions and, therefore, require the more terms in the series expansion. The cracked configurations with distributed loadings are less sensitive to the number of terms in Williams series expansion. As a whole, it is demonstrated that high order terms have principal role in the description of the stress-strain in the vicinity of the crack tip.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128382953","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}
{"title":"DETERMINATION OF MECHANICAL PROPERTIES OF A MATERIAL MODELED USING THE MOLECULAR DYNAMICS METHOD","authors":"O. Belova","doi":"10.18287/2541-7525-2021-27-4-14-21","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-4-14-21","url":null,"abstract":"The article discusses a method for determining the elastic constants of a material modeled using the molecular dynamics method in the LAMMPS package (Large-scale Atomic/Molecular Massively Parallel Simulator). The purpose of the study is to calculate the matrix of elastic constants Cij or the compliancecoefficients Sij of materials. Knowing them, elastic modulus is calculated along certain directions and shear in shear systems, as well as the Poissons ratio. Extreme values of mechanical constants can be calculated. In addition, linear combinations of elastic constants that have a physical meaning can be determined. FCC single crystals of copper and aluminum were selected as examples for modeling. The ELATE - Elastic tensoranalysis computational and graphical package is used to visualize elastic properties.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128981522","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}
{"title":"ON THE NATURE OF ADDITIONAL SPACE AT CUTTING OF SPACES OF CUSP FORMS","authors":"G. V. Voskresenskaya","doi":"10.18287/2541-7525-2021-27-4-7-13","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-4-7-13","url":null,"abstract":"In the article we study a space of cusp forms by the method of cutting. This space is a direct sum of the subspace of forms divided by the fixed cusp form named the cutting function and the additional space. If the additional space is zero we have the situation of exact cutting. In common case the cutting is not exact and it is important to research the nature of the additional space. We prove that the basis of the additional space can be described by the space of cusp forms of small weight. This weight is not more than 14 and often is equal to 4. We give examples of all cutting functions for all levels. We prove the theorem about the basis of the additional space to the space of cusp forms in the space of modular forms of the same level, weight and character. We use properties of eta-products, Biagioli formula for orders in cusps and Cohen Oesterle formula for dimensions.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126151032","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}
D. V. Veniosov, S. S. Stekolshchikov, A. V. Shirokov
{"title":"AUTOMATION OF DESIGN AND CALCULATION OF THE HYDRAULIC TURBINE DISTRIBUTOR","authors":"D. V. Veniosov, S. S. Stekolshchikov, A. V. Shirokov","doi":"10.18287/2541-7525-2021-27-4-22-29","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-4-22-29","url":null,"abstract":"The article describes the algorithm for calculating a distributor of hydraulic turbine, which includes three stages: calculation of the kinematic characteristics of the distributor of hydraulic turbine, strength calculation of the guide vane and calculation of the power characteristics of the drive. Software implementing the specified algorithm has been developed. The use of software in JSC TYAZHMASH (Syzran) made it possible to reduce the labor intensity and cost of designing a distributor of hydraulic turbine.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132709714","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}
{"title":"EVALUATION OF THE APPLICATION OF DOUBLE-EXPOSURE SPECKLE PHOTOGRAPHY WITH DIFFERENT APERTURES IN EXPERIMENTAL MECHANICS","authors":"M. N. Osipov, R. N. Sergeev","doi":"10.18287/2541-7525-2021-27-4-83-91","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-4-83-91","url":null,"abstract":"The article presents an experimental evaluation of the use of double-exposure speckle photography with circular and annular apertures in experimental mechanics using the example of determining the modulus of elasticity in tension. The description of the process of registration of speckle photography and its subsequent processing is given. Based on the results of calculations of the finite element model of the sample, the areawhere the boundary conditions do not affect its tension is determined. A description is given of the procedure for processing speckle photographs to determine the modulus of elasticity and the error in its measurement with different apertures.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134441900","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}
{"title":"MOLECULAR DYNAMIC MODELING OF STRESS FIELDS IN PLATES WITH A CENTRAL CRACK MADE OF MATERIALS WITH A FACE-CENTERED CUBIC LATTICE","authors":"K. A. Mushankova, L. Stepanova","doi":"10.18287/2541-7525-2021-27-4-68-82","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-4-68-82","url":null,"abstract":"The purpose of this study is to determine the stress-strain state at the atomistic level using molecular dynamic modeling of the structure of the material, which were selected as single crystals of copper and aluminium. A series of computational experiments were carried out on plates with a central crack in the LAMMPS open code. Also, LAMMPS conducted experiments on cubic samples from the same materials to find the tensor components of elastic modules. The visualizations obtained in the OVITO software package are shown, which show the distribution of stress tensor components over different time steps for copper and aluminum single crystals. The work presents graphs showing the dependence of the stress tensor components on the polar angle, obtained by atomistic and classical approaches. The comparison showed that the stressfields at the nanoscale level are in good agreement with their macroscopic magnitudes, so a continuum approach can be applied at the atomistic level.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131454424","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}
{"title":"APPLICATION OF THE UMAT SUBROUTINE FOR SOLVING CONTINUUM MECHANICS PROBLEMS (OVERVIEW)","authors":"O. Belova, D. V. Chapliy, L. Stepanova","doi":"10.18287/2541-7525-2021-27-3-46-73","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-3-46-73","url":null,"abstract":"This paper presents an overview of the application of the UMAT subroutine of the SIMULIA Abaqus multifunctional software package in solid mechanics and related areas. This subroutine is used to describe new user materials that are not available in the class of standard materials of the SIMULIA Abaqus package. This overview article provides examples of problems and constitutive equations of materials that are modeled using UMAT / VUMAT procedures. Various types of materials are presented, successfully described by means of user-defined UMAT and VUMAT procedures. A general description and experience of using the UMAT subroutine is given. The results of finite element modeling of the deformation of aplate weakened by a central circular hole under uniform and uniaxial tension with steady-state creep in a damaged medium evolving according to a power law are presented in the coupled formulation of the problem (creep - damage). The distributions of stresses, strains, and damage fields at the tip of the defect under creep conditions are found, and an analysis is made of the effect of the damage accumulation process on the stress fields at the crack tip under steady-state creep conditions. The distributions of stresses and creep strains are demonstrated taking into account the accumulation of damage over time.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123877376","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}
{"title":"DECOMPOSITION OF ENZYME KINETICS SYSTEM WITH FAST AND SLOW VARIABLES IN SUICIDE SUBSTRATE PROBLEM","authors":"M. A. Smetannikov","doi":"10.18287/2541-7525-2021-27-3-83-88","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-3-83-88","url":null,"abstract":"In this paper an example of cooperative phenomenon, in which the substrate is known as suicide substrate, because it binds to the active enzyme as a substrate, inactivates because enzyme turns it into an inhibitor and provides an irreversible reaction is considered. In this case the substrate commits suicide. The aim of the work is to apply the method of integral manifolds to the reduction of the system of kinetics of suicide substrate. Work describes in detail the rationale for the decomposition algorithm of the enzyme kinetics problem for dynamical systems with fast and slow variables and the construction of integral manifolds for such systems, this article presents the results of applying the above methods to systems of the suicide substrate kinetics and compares solutions for four equations graphically. Comparisons of solutions for four equations are given graphically, the graphs are created using Microsoft Excel.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121619018","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}
{"title":"ON DISCRETE SYSTEMS WITH POTENTIAL OPERATORS","authors":"V. Savchin, P. Trinh","doi":"10.18287/2541-7525-2021-27-3-74-82","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-3-74-82","url":null,"abstract":"The main purpose of this work is to study the potentiality of a discrete system obtained from the system of the form C(t, u)u_ (t)+E(t, u) = 0 with continuous time. The definition of potentiality of the corresponding discrete system is introduced. Necessary and sufficient conditions for its potentiality with respect to a given bilinear form are obtained. The algorithm for the construction of the corresponding functionalthe analogue of the Hamiltonian actionis presented. The illustrative example is given.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125878374","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}