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Об одном подходе к аналитическому решению задачи экструзии труб при наличии внутреннего высокого давления 在内部高压下分析管挤压问题的一种方法
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-09-30 DOI: 10.54503/0002-3051-2022.75.3-55
М. А. Маргарян
{"title":"Об одном подходе к аналитическому решению задачи экструзии труб при наличии внутреннего высокого давления","authors":"М. А. Маргарян","doi":"10.54503/0002-3051-2022.75.3-55","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.3-55","url":null,"abstract":"Based on the assumption that external v p and internal r p pressures acting on the pipe are equal: the circumferential stress of the pipe is determined. Simplified plasticity condition is obtained and the stress-strain state of the pipe is investigated by the analytical method. The problem of extrusion of pipes loaded with internal high pressure is firstly completely solved in the case of the presence of friction, and then by a fairly simplified method in the absence of friction. This is due to the fact that in the main case, in the denominator of the formula for determining the Ϭm meridional stress, there is a coefficient, that takes into account friction, and in the case of k = 0 it is impossible to immediately determine the corresponding formula for the case in the absence of friction. To implement this process, the formula of the meridional stress was transformed to obtain an exponential function and its representation in the form of a series. Dimensionless meridional, circumferential and average stresses are determined, depending on the degree of pipe deformation, which makes it possible to use the formulas of the deformation theory of plasticity of porous materials to study the process of compaction of the pipe material. Numerical calculations are carried out in the MS EXCEL software environment for various coefficients of friction at 10% of the initial porosity of the material. To obtain a fully compacted material of a sintered pipe, the process of extrusion of the pipe with various dimensions is modeled in a corresponding conical die.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127609745","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}
引用次数: 0
Shear elastic waves in bi-material multi-layered waveguide 双材料多层波导中的剪切弹性波
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-09-30 DOI: 10.54503/0002-3051-2022.75.3-42
K. Ghazaryan, R. Ghazaryan, S. Terzyan
{"title":"Shear elastic waves in bi-material multi-layered waveguide","authors":"K. Ghazaryan, R. Ghazaryan, S. Terzyan","doi":"10.54503/0002-3051-2022.75.3-42","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.3-42","url":null,"abstract":"This analytical study demonstrates shear elastic wave propagation in stratified waveguide with emphasis on wave localisation effects using the propagator matrix method. The stratified waveguide consists of two-phase piecewise homogeneous periodically arranged finite number sub-layers along waveguide thickness. Analytical solutions are carried out for traction free waveguide. The existence of two modal types of guided waves is established: i) a localised surface mode occurring in “stopband” and ii) normal modes arising in a “passband” of frequencies.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122266556","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}
引用次数: 0
Контактная задача об осесимметричном кручении упругого слоя посредством цилиндрического штампа 轴对称弹性层通过圆柱形冲压的接触问题
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-09-30 DOI: 10.54503/0002-3051-2022.75.3-20
А. В. Гаспарян, С. М. Мхитарян, А. В. Саакян
{"title":"Контактная задача об осесимметричном кручении упругого слоя посредством цилиндрического штампа","authors":"А. В. Гаспарян, С. М. Мхитарян, А. В. Саакян","doi":"10.54503/0002-3051-2022.75.3-20","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.3-20","url":null,"abstract":"The paper studies the axis-symmetric contact problem between an elastic layer and a rigid cylindrical circular stamp under torque. The stamp adheres to the upper boundary of the layer whereas the lower boundary of the layer is rigidly fastened. With the application of Hankel integral transform solving the problem reduces to solving the first kind Fredholm integral equation (IE) with symmetrical kernel, represented as a sum of its principal part, Weber-Sonin integral, and the regular kernel. It is estimated that once its height attains a certain level, the layer actually deforms as a semi-space. In the process, through Abel IE method, the solution of the well-known Reissner-Sagoci problem is obtained once again and the original first kind Fredholm IE is reduced to the second kind Fredholm IE. Concurrently, using the collocation method combined with Gauss type quadrature formulas for integral estimation, the original IE reduces to a finite system of linear algebraic equations. To obtain this quadrature formula, properties of Gegenbauer and Chebyshev orthogonal polynomials are used. In the enough wide range of change of characteristic elastic and geometrical parameters of the problem numerical analysis is performed and patterns of changes of tangential contact stresses under the stamp as well as the angle of twist of the stamp are identified.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133695095","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}
引用次数: 1
Распространение плоских волн в упругой полуплоскости, усиленной по своей границе накладкой бесконечной длины 平面在弹性半平面上的传播，在其边界上增加了无限长度的填充物
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-09-30 DOI: 10.54503/0002-3051-2022.75.3-7
К. Л. Агаян
{"title":"Распространение плоских волн в упругой полуплоскости, усиленной по своей границе накладкой бесконечной длины","authors":"К. Л. Агаян","doi":"10.54503/0002-3051-2022.75.3-7","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.3-7","url":null,"abstract":"The dynamic contact problem of the propagation of plane elastic waves incident from infinity onto the boundary of an elastic half-plane reinforced by an infinite plate of small thickness is studied. Questions related to the dynamic mutual influence of an elastic half-plane with an stringer attached to its boundary are studied. As a physical model for the stringer, a one-dimensional elastic continuum model is taken. The solution of the problem is constructed by direct application of the Fourier transform. Analytical expressions are obtained that represent the distribution of wave components in all parts of the half-plane.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116831727","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}
引用次数: 1
Сверхзвуковой флаттер удлиненной прямоугольной пластинки с одним свободным краем, растянутой по потоку газа 超声速长方形唱片颤振，在气体流中有一个自由边缘。
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-09-30 DOI: 10.54503/0002-3051-2022.75.3-64
С. Р. Мартиросян
{"title":"Сверхзвуковой флаттер удлиненной прямоугольной пластинки с одним свободным краем, растянутой по потоку газа","authors":"С. Р. Мартиросян","doi":"10.54503/0002-3051-2022.75.3-64","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.3-64","url":null,"abstract":"In the article, in a linear formulation, the influence of the initial stress state of an elongated rectangular elastic plate with one free edge, stretched along the gas flow, on the stability of the unperturbed motion of the \"plate-flow\" linear dynamic system is studied under the assumption that there are concentrated inertial masses on its free edge and moments. An analytical solution of the problem of stability of a dynamical system is obtained. The stabilizing effect of tensile forces on the system is shown.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115248567","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}
引用次数: 1
О некоторых аспектах развития теории оболочек и пластин в Армении 亚美尼亚壳板理论发展的某些方面
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-05-30 DOI: 10.54503/0002-3051-2022.75.1-2-5
Л. А. Агаловян
{"title":"О некоторых аспектах развития теории оболочек и пластин в Армении","authors":"Л. А. Агаловян","doi":"10.54503/0002-3051-2022.75.1-2-5","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.1-2-5","url":null,"abstract":"Излагаются некоторые аспекты развития классической, уточненных, асимптотической теорий анизотропных пластин и оболочек в Армении. Отмечается решающая роль С.А. Амбарцумяна в создании и развитии этих теорий, основании соответствующей Научной школы.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129925135","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}
引用次数: 0
Multi-Component Electroacoustic Waves (Mceaw) In Piezo Crystalline Textures: Applied Opportunities 多分量电声波(Mceaw)在压电晶体结构:应用机会
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-05-25 DOI: 10.54503/0002-3051-2022.75.1-2-111
A. Avetisyan
{"title":"Multi-Component Electroacoustic Waves (Mceaw) In Piezo Crystalline Textures: Applied Opportunities","authors":"A. Avetisyan","doi":"10.54503/0002-3051-2022.75.1-2-111","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.1-2-111","url":null,"abstract":"In this paper is shown, that in each sagittal plane of the piezoelectric texture, both the one-component elastic shear wave and the two-component elastic plane deformation wave can be accompanied by either oscillations of the transverse component of the electric field or oscillations of the plane electric field. Four such packets of multicomponent electroelastic waves are formed.Necessary and sufficient conditions are obtained that allow the formulation of a two-dimensional problem of electroelasticity in a vibrated sagittal plane of a piezocrystal, where separate excitation and propagation of a multicomponent quasistatic electroelastic wave is possible.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132731582","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}
引用次数: 1
О коэффициентных обратных задачах и их приложениях в механике и биомеханике 系数反问题及其在力学和生物力学中的应用
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-05-25 DOI: 10.54503/0002-3051-2022.75.1-2-36
А. О. Ватульян
{"title":"О коэффициентных обратных задачах и их приложениях в механике и биомеханике","authors":"А. О. Ватульян","doi":"10.54503/0002-3051-2022.75.1-2-36","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.1-2-36","url":null,"abstract":"Рассмотрены различные типы коэффициентных обратных задач для операторов с переменными коэффициентами, их приложения к задачам идентификации неоднородных структур - функционально- градиентных материалов на примере стержневых и цилиндрических тел при снятии дополнительной информации с поверхности или торца. Представлено приложение к задачам эластографии при идентификации свойств мягких тканей при дополнительной информации внутри объекта.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133792327","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}
引用次数: 0
Averaged Controllability Of Transversely Isotropic Ambartsumyan Plate 横观各向同性阿姆巴苏木板块的平均可控性
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-05-25 DOI: 10.54503/0002-3051-2022.75.1-2-124
A. Avetisyan, H. Jilavyan, A. Khurshudyan
{"title":"Averaged Controllability Of Transversely Isotropic Ambartsumyan Plate","authors":"A. Avetisyan, H. Jilavyan, A. Khurshudyan","doi":"10.54503/0002-3051-2022.75.1-2-124","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.1-2-124","url":null,"abstract":"In this paper we study the averaged controllability of Ambartsumyan plate made of a transversely isotropic material. Governing equations are based on assumptions of particular theory of anisotropic plates developed by S. A. Ambartsumyan specifically for describing the deformation of anisotropic plates made of material with isotropy plane which, at each point of the plate, is parallel to its middle plane. The Green’s function approach is applied to express the plate normal displacement by means of material parameters (density, Young moduli in both directions of isotropy) which are assumed to be uniformly distributed random variables. Eventually, the averaged controllability condition is reduced to an infinite system of linear constraints with respect to the control action. Three types of particular (heuristic) solutions of the truncated version of the infinite system are discussed. Determination of control parameters is reduced to the solution of a problem of nonlinear programming.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121192674","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}
引用次数: 0
О точном решении одного класса задач о контактном взаимодействии стрингеров с упругими телами 关于一个问题的精确解，关于斯金格和弹性身体的接触作用。
Mechanics - Proceedings of National Academy of Sciences of Armenia Pub Date : 2022-05-25 DOI: 10.54503/0002-3051-2022.75.1-2-48
М. С. Григорян, С. М. Мхитарян
{"title":"О точном решении одного класса задач о контактном взаимодействии стрингеров с упругими телами","authors":"М. С. Григорян, С. М. Мхитарян","doi":"10.54503/0002-3051-2022.75.1-2-48","DOIUrl":"https://doi.org/10.54503/0002-3051-2022.75.1-2-48","url":null,"abstract":"В модифицированной постановке задач о контактном взаимодействии тонкостенных элементов в виде стрингеров с массивными упругими телами, когда заранее задан режим упругих горизонтальных перемещений точек стрингеров, рассмотрен один класс таких задач, решаемых точно. Эти задачи представляют теоретический и практический интерес при исследовании вопросов жесткости систем стрингеры - упругие основания с последующим определением действующих на стрингеры силовых факторов, обеспечивающих заданный их режим упругих перемещений. Массивные упругие тела берутся в виде полуплоскости, полосы и клина, находящихся в условиях плоской или антиплоской деформации. Решения рассматриваемых контактных задач сведены к интегральным уравнениям Фредгольма первого рода с симметрическим логарифмическим ядром. Их точные (замкнутые) решения построены при помощи спектральных соотношений для многочленов Чебышева.","PeriodicalId":399202,"journal":{"name":"Mechanics - Proceedings of National Academy of Sciences of Armenia","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115471497","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}
引用次数: 0
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