Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics最新文献

{"title":"Simulation of the stress state in barriers made of anisotropic materials","authors":"M. Krivosheina","doi":"10.17223/19988621/79/8","DOIUrl":"https://doi.org/10.17223/19988621/79/8","url":null,"abstract":"To study the properties of anisotropic materials, a mathematical model is proposed that accounts for the anisotropy of elastic and plastic properties, as well as the anisotropy of “thermal” and “cold” components of pressure. The model is applied in a threedimensional simulation of the deformation of an HCP-single-crystal barrier under impact loading by an aluminum impactor. The numerical simulation results are obtained using the dynamic finite element method with a difference scheme modified to account for the anisotropy of “cold” and “thermal” pressure components. To simulate the anisotropy of the stress deviator in the region of elastic deformations, generalized Hooke's law is used, while in the region of plastic deformations, the Mises-Hill plasticity function (Hill48) is used with account for the anisotropy of elastic properties and anisotropy of the Gruneisen coefficient. The experimentally and numerically obtained velocity profiles of the back surfaces of single-crystal zinc barriers during the spall fracture are compared with each other. When the impact loading direction coincides with [0001] axis, the elastic precursor is not observed on the velocity profile calculated numerically, which is the same for the one derived experimentally. This effect may be explained only with the use of anisotropic pressur.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79183305","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":"Analysis of a dynamic structure of secular resonances in circumlunar orbital space","authors":"N. Popandopulo, A. Aleksandrova, T. Bordovitsyna","doi":"10.17223/19988621/77/9","DOIUrl":"https://doi.org/10.17223/19988621/77/9","url":null,"abstract":"When developing new circumlunar satellite systems for various purposes, it is necessary to know the dynamic features of various regions of circumlunar space. It is noted that one of the main features of the dynamics of artificial Moon satellites (AMS) is the increase in the eccentricity of their orbits. It is known that such orbital evolution of objects can be caused by resonant perturbations. In this regard, the purpose of this paper is to study the influence of secular and half-secular resonances occurring on the AMS. The results are obtained by means of the processing of data from an extensive numerical experiment to study the orbital evolution of the uniformly distributed circumlunar objects moving in the range of large semi-axes from 1911.8 to 26070 km and with inclinations from 0 to 180°. The study of the influence of secular and half-secular resonances on the orbital evolution of the AMS is carried out using numerical and analytical techniques. Both techniques have advantages and disadvantages and are used in the study. Maps of secular and half-secular resonances are of great practical importance. They clearly demonstrate the areas of influence of secular resonances on the orbital evolution of circumlunar objects depending on the initial values of the semimajor axis and inclination of the orbits of objects. The analysis of each particular resonance consists in the revealing of a resonant characteristic type, which is determined by the nature of the change in a critical argument: libration - stable resonance, libration/circulation - unstable resonance, and circulation - no resonance. To estimate the whole range of the influence of resonances on the AMS dynamics, maps of their overlaps are built. The maps allow one to determine areas with significant influence of the resonances on the orbital evolution of circumlunar objects. The obtained results show that the reason for a large increase in the eccentricity in a vast area of circumlunar orbital space is the presence of the stable apsidal resonance of the Kozai-Lidov type.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75485326","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":"Prediction of durability of soldered contact joints of chips","authors":"A. Azin, Nikolay Maritsky, S. Ponomarev, Sergey V. Rikkonen","doi":"10.17223/19988621/76/4","DOIUrl":"https://doi.org/10.17223/19988621/76/4","url":null,"abstract":"The study is aimed at developing a nondestructive testing method for electronic equipment and its components. This method allows one to identify critical design defects of printed circuit boards (PCB) and to predict their service life taking into account the nature of probable operating loads. The study uses an acoustic emission method to identify and localize critical design defects of printed circuit boards. Geometric dimensions of detected critical defects can be determined by X-ray tomography. Based on the results of the study, a method combining acoustic emission and X-ray tomography has been developed for nondestructive testing of printed circuit boards. The stress-strain state of solder joints containing detected defects is analyzed. Durability is predicted using the damage function of the material, experimental fatigue curve with allowance for rheological properties of materials, the temperature effects, and complex stress-strain state. The results of using the developed method for estimating the degree of damage of the electronic board have been verified based on the experimental results of studies carried out in accordance with IPC-9701. The prediction error does not exceed 5%. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86952176","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":"A new processing algorithm for photoelasticity method data","authors":"Aleksey V. Likhachev, M. Tabanyukhova","doi":"10.17223/19988621/79/9","DOIUrl":"https://doi.org/10.17223/19988621/79/9","url":null,"abstract":"The photoelasticity method is a reliable tool for studying the stress state of flat elements in building structures using the models made of optically sensitive materials. In this paper, the classical photoelasticity is considered. The experimental data obtained with the use of the method are presented as interferograms. A decoding procedure implies the obtaining of some normal and tangential stress values in the plane of the model. The polarization-projection installations that are used in optical methods are rather simple. However, the digital processing of the images obtained during the loaded model transmission requires high-intelligent software. Nowadays, national and international laboratories, working with polarization-optical methods, strive to develop digital photoelasticity. For some reasons, the authors of the presented work needed to develop their own algorithms for decoding experimental data of the photoelasticity method. This work is mainly devoted to a formulation of the problems to be solved. Some of them have already been solved, and the results obtained are presented here. The authors place special emphasis on the description of the algorithm for tracing of interference fringes based on the analysis of the image gradient.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79256429","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":"Formal derivation of mechanical motion magnitudes","authors":"V. Pavlov","doi":"10.17223/19988621/78/11","DOIUrl":"https://doi.org/10.17223/19988621/78/11","url":null,"abstract":"Quantum-mechanical differential equations are considered, which are formal analogues of the Schrödinger equation. Their differences from each other and from the Schrödinger equation lie in the orders of partial derivatives. A characteristic feature of these equations is the presence of dimensional coefficients, which are the product of integer powers of mass and velocity, which allows us to consider them as quantities of mechanical motion. The logical regularity of the formation of these values is established. The applied nature of two of them - the integral Umov vector for kinetic energy and backward momentum - is considered.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73198662","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 the elastic fields induced by body forces in transtropic bodies of revolution","authors":"D. A. Ivanychev","doi":"10.17223/19988621/77/7","DOIUrl":"https://doi.org/10.17223/19988621/77/7","url":null,"abstract":"The paper presents a method for determining the stress-strain state of transversely isotropic bodies of revolution under the action of non-axisymmetric stationary body forces. This problem solution involves the use of boundary state method definitions. The basis of the space of internal states is formed using the fundamental polynomials. The polynomial is placed in any position of a displacement vector of the plane auxiliary state; the spatial state is determined by transition formulas. A set of such states forms a finite-dimensional basis, in which after orthogonalization, the desired state is expanded into Fourier series with the same coefficients. The series coefficients are scalar products of the vectors of given and basic body forces. Finally, the determination of the elastic state is reduced to solving quadratures. The solutions to problems of elasticity theory for a transversely isotropic circular cylinder are analyzed in terms of the action of body forces given by various cyclic laws (sine and cosine). Recommendations are given for constructing the basis of internal states depending on the type of the function of the given body forces. The analysis of the series convergence and the estimation of the solution accuracy are given in a graphical form.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75244667","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":"A study of the structure and properties of the metal matrix composite materials obtained by a method of direct laser growing","authors":"V. Promakhov, A. Matveev, N. Schulz, V. Bakhmat, F. Dronov, Timur E. Turanov","doi":"10.17223/19988621/77/10","DOIUrl":"https://doi.org/10.17223/19988621/77/10","url":null,"abstract":"Due to mechanical properties, Inconel family alloys are proven to be functional materials that are used at elevated temperatures in chemically aggressive environments and under high loads. Development of additive technologies has revealed a potential of these alloys as an initial powder raw material for additive manufacturing machines. In this work, the application of metal matrix composite materials in a direct laser growing technology is studied. The technology of self-propagating high-temperature synthesis is used to manufacture the composite material. The study results show that the application of metal matrix materials in the technology of direct laser growing allows one to increase wettability of ceramic particles by a matrix metal. As a result, the quality of particle-matrix borders is improved, the porosity is decreased, and the uniformity of the distribution of particles in the matrix is increased. The structure of the obtained materials is represented by Inconel 625 matrix alloy and inclusions of TiB2 ceramics. The average size of the ceramic particles is less than 300 nm. It is shown that adding to Inconel 625 powder of a composite metal matrix SHS powder of NiTi-TiB2 in an amount of 5 wt% leads to an increase in the microhardness of the material by 1.5 times relative to the materials obtained from pure Inconel 625. At the same time, there is an increase in the ultimate strength of the materials up to 920 MPa and a decrease in the ductility by 15% relative to the samples made of pure Inconel 625 alloy.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75424237","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 combustion of particles of boron, boron carbide, boron nitride and carbon in air","authors":"S. Rashkovskiy, A. V. Fedorychev, Y. Milekhin","doi":"10.17223/19988621/75/11","DOIUrl":"https://doi.org/10.17223/19988621/75/11","url":null,"abstract":"Combustion models of main components of condensed combustion products (CCP) of boron-containing solid propellants: boron, boron carbide, boron nitride, and carbon are analyzed. Using the known experimental data, the parameters of the combustion model of boron carbide and boron nitride particles are determined. Using the models of combustion of boron, B4C, BN and carbon particles, parametric calculations of the combustion of both individual abovementioned particles and their mixture, which simulates the composition of the CCP of boron-containing solid propellant, have been carried out. Calculations have shown that combustion of BN has the least effect on the completeness of CCP combustion. This is due to its low calorific value and low content in CCP. Ceteris paribus, carbon particles burn the fastest; however, their contribution to the completeness of CCP combustion is less than that of boron and boron carbide due to their lower calorific value.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73578798","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 shape of the brachistichrone rotating in a vertical plane","authors":"S. Gladkov, S. B. Bogdanova","doi":"10.17223/19988621/78/7","DOIUrl":"https://doi.org/10.17223/19988621/78/7","url":null,"abstract":"The paper aims to study the influence of the brachistochrone rotating in its own plane on the gutter shape along which a body moves. The problem is solved with a moving basis, which allows one to account for all forces exerted on the body. Introduction of the moving basis yields a compact system of dynamical equations, whose validity was proven in previous author's papers. In limiting cases, such an approach is used to solve analytically the obtained equations of motion and to determine the shape of curves depending on the parameters in the equations by tabular integration. The latter is illustrated in the figures presented. According to the energy conservation law, which accounts for the rotation of the entire system as a whole, the resulting equations also include the angular frequency of rotation as an additional parameter. In this paper, the case of steady rotation is studied. Such conditions have a significant impact on the brachistochrone. In the limiting case of low rotational speeds, the curve, as it should be, degenerates smoothly into a classical brachistochrone, which is justified by the numerical methods used.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77558343","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":"Exact solution of the fundamental equation of acoustics for a pressure wave developing in two directions","authors":"V. Borodin, A. Lun-Fu, M. Bubenchikov, A. Bubenchikov, D. Mamontov","doi":"10.17223/19988621/79/1","DOIUrl":"https://doi.org/10.17223/19988621/79/1","url":null,"abstract":"The authors proceed from the hyperbolic equation for acoustic pressure. Using the integral Fourier transform along the axial coordinate, an equation in partial derivatives for the kernel of this transformation is found. This equation contains only one spatial coordinate and time. Applying the integral Laplace transform in time to the last equation, we obtain an ordinary differential equation with respect to the radial coordinate for the corresponding image. It turns out that the solution of the last equation is the well-known Macdonald function. For this function, it was possible to find the original image according to Laplace. All this made it possible to write an integral formula for the pressure in a sound wave. If the function of the initial pressure distribution along the pipe axis is taken in the form of a Gaussian impulse, then the integrals included in the representation of the desired solution are taken explicitly. As a result, we obtain an explicit compact formula for the acoustic pressure distribution in the axisymmetric case. It is convenient to use this formula to analyze the distribution of sound disturbances both along the pipe axis and in the radial direction. Therefore, the results are presented as isobars in the (z, r) plane corresponding to different times.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89697370","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}