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Pmm Journal of Applied Mathematics and Mechanics最新文献

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The solution of a certain class of dual integral equations with the right-hand side in the form of a Fourier series and its application to the solution of contact problems for inhomogeneous media 一类右手边为傅里叶级数的对偶积分方程的解及其在非齐次介质接触问题中的应用
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-05-08 DOI: 10.1016/j.jappmathmech.2018.03.018
S.M. Aizikovich, S.S. Volkov, B.I. Mitrin
{"title":"The solution of a certain class of dual integral equations with the right-hand side in the form of a Fourier series and its application to the solution of contact problems for inhomogeneous media","authors":"S.M. Aizikovich,&nbsp;S.S. Volkov,&nbsp;B.I. Mitrin","doi":"10.1016/j.jappmathmech.2018.03.018","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.018","url":null,"abstract":"<div><p><span><span>Using the bilateral asymptotic method, a semi-analytical solution of a dual integral equation with its right-hand side in the form of a </span>Fourier series is constructed. This equation arises in the solution of a number of contact problems of </span>elasticity theory<span> for bodies with inhomogeneous coatings. The efficiency of the method is illustrated in the example of the solution of the plane contact problem on bending of a beam lying on a functionally graded strip with arbitrary variation of the elastic moduli with depth. It is assumed that the strip is perfectly bonded to an elastic half-plane. Numerical results are presented for a strip whose Young's modulus varies harmonically with depth. In this case, Young's modulus of the substrate is 100 times greater than at the lower boundary of the coating.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 6","pages":"Pages 486-491"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91672358","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: 3
Variational formulation of dynamic problems for a nonlinear Cosserat medium 非线性Cosserat介质动力学问题的变分公式
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2017-08-14 DOI: 10.1016/j.jappmathmech.2017.07.007
E.V. Zdanchuk, V.V. Kuroyedov, V.V. Lalin, I.I. Lalina, E.A. Provatorova
{"title":"Variational formulation of dynamic problems for a nonlinear Cosserat medium","authors":"E.V. Zdanchuk,&nbsp;V.V. Kuroyedov,&nbsp;V.V. Lalin,&nbsp;I.I. Lalina,&nbsp;E.A. Provatorova","doi":"10.1016/j.jappmathmech.2017.07.007","DOIUrl":"10.1016/j.jappmathmech.2017.07.007","url":null,"abstract":"<div><p><span>A variational formulation of </span>dynamic problems<span><span> for a geometrically and physically nonlinear elastic Cosserat medium is obtained in the form of the problem of finding the stationary point of Hamilton's functional. Variations of the strain and rotation tensors and the linear and angular velocity<span> vectors are calculated. The equivalence of the Euler equations with </span></span>natural boundary conditions<span> to the equations of motion with the original boundary conditions in the case of potential force and torque loads is proved. A nontrivial potentiality condition of the torque (bulk and surface) loads is obtained.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 66-70"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87716699","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: 2
Stabilization of the preset motions of a holonomic mechanical system without velocity measurement 无速度测量的完整机械系统预置运动的稳定
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2017-09-28 DOI: 10.1016/j.jappmathmech.2017.08.003
A.S. Andreev, O.A. Peregudova
{"title":"Stabilization of the preset motions of a holonomic mechanical system without velocity measurement","authors":"A.S. Andreev,&nbsp;O.A. Peregudova","doi":"10.1016/j.jappmathmech.2017.08.003","DOIUrl":"10.1016/j.jappmathmech.2017.08.003","url":null,"abstract":"<div><p>Problems on the stabilization of the preset positions and steady motions of holonomic mechanical systems, measuring only the generalized coordinates, are investigated. The novelty of the results lies in the construction of control actions that solve the above problems in a fairly general formulation. Problems concerning the stabilization of the preset positions and steady motions of a heavy rigid body with a fixed point and the preset positions of a two-link manipulator with three degrees of freedom are solved as specific applications of the theoretical results obtained.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 2","pages":"Pages 95-105"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.08.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84889022","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: 19
On methods for increasing the margin of stability of motion of optimum bodies 提高最优体运动稳定裕度的方法
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/J.JAPPMATHMECH.2018.03.015
G. Yakunina
{"title":"On methods for increasing the margin of stability of motion of optimum bodies","authors":"G. Yakunina","doi":"10.1016/J.JAPPMATHMECH.2018.03.015","DOIUrl":"https://doi.org/10.1016/J.JAPPMATHMECH.2018.03.015","url":null,"abstract":"","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"24 1","pages":"463-472"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85101070","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
Characteristic features of the process of wear of a punch and a thin elastic strip with non-uniform friction and wear parameters 具有非均匀摩擦磨损参数的冲头和薄弹性条磨损过程的特征特征
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/J.JAPPMATHMECH.2018.03.019
I. Soldatenkov
{"title":"Characteristic features of the process of wear of a punch and a thin elastic strip with non-uniform friction and wear parameters","authors":"I. Soldatenkov","doi":"10.1016/J.JAPPMATHMECH.2018.03.019","DOIUrl":"https://doi.org/10.1016/J.JAPPMATHMECH.2018.03.019","url":null,"abstract":"","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"85 1","pages":"492-498"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72682562","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
Bifurcation diagram of the self-sustained oscillation modes for a system with dynamic symmetry 动态对称系统的自持续振荡模态分岔图
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-05-08 DOI: 10.1016/j.jappmathmech.2018.03.012
L.A. Klimina, B. Ya. Lokshin, V.A. Samsonov
{"title":"Bifurcation diagram of the self-sustained oscillation modes for a system with dynamic symmetry","authors":"L.A. Klimina,&nbsp;B. Ya. Lokshin,&nbsp;V.A. Samsonov","doi":"10.1016/j.jappmathmech.2018.03.012","DOIUrl":"10.1016/j.jappmathmech.2018.03.012","url":null,"abstract":"<div><p><span><span>An autonomous dynamical system with one degree of freedom is considered which possesses properties such that an asymptotically </span>stable equilibrium<span> becomes unstable after a certain parameter passes through zero and two new symmetrically arranged equilibria are created alongside it. It is known that, for sufficiently small values of the above mentioned parameter, bifurcation can be accompanied by the occurrence of periodic trajectories (cycles). To describe them, a bifurcation diagram of the relation between the amplitude of the cycles and the parameter, which characterizes the dissipation and takes finite values, is constructed. The results obtained are illustrated using the example of an investigation of the self-induced oscillatory modes in a model of an aerodynamic pendulum that takes account of the displacement of the pressure centre when the </span></span>angle of attack is changed.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 6","pages":"Pages 442-449"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91304062","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: 5
Elastic seepage in a fracture located in an oil or gas reservoir 弹性渗漏:位于石油或天然气储层的裂缝中的弹性渗漏
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2017-10-07 DOI: 10.1016/j.jappmathmech.2017.08.013
Z.M. Nagaeva , V.Sh. Shagapov
{"title":"Elastic seepage in a fracture located in an oil or gas reservoir","authors":"Z.M. Nagaeva ,&nbsp;V.Sh. Shagapov","doi":"10.1016/j.jappmathmech.2017.08.013","DOIUrl":"10.1016/j.jappmathmech.2017.08.013","url":null,"abstract":"<div><p>Problems concerning the extraction of the fluid from an oil well under conditions of a constant pressure drop<span> or a constant flow rate are considered on the basis of a model describing a seepage flow in a fracture located in an oil or gas reservoir. Exact solutions are obtained and, on the basis of these solutions, the effect of the collecting characteristics of the reservoir and the fracture is analysed as well as the effect of the rheological properties of the saturating fluid on the evolution of the pressure in the fracture, the output from the oil well and the dynamics of the pressure in the oil well.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 3","pages":"Pages 214-222"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.08.013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87473519","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: 11
Modelling of a continuously inhomogeneous coating of an elastic sphere by a system of homogeneous elastic layers in the problem of sound scattering 用均匀弹性层系统模拟声散射问题中弹性球的连续非均匀涂层
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-05-08 DOI: 10.1016/j.jappmathmech.2018.03.017
L.A. Tolokonnikov
{"title":"Modelling of a continuously inhomogeneous coating of an elastic sphere by a system of homogeneous elastic layers in the problem of sound scattering","authors":"L.A. Tolokonnikov","doi":"10.1016/j.jappmathmech.2018.03.017","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.017","url":null,"abstract":"<div><p><span><span>On the basis of analytical solutions of problems on the diffraction of a plane sound wave on a homogeneous elastic sphere with a discretely layered coating and with a continuously-inhomogeneous coating, the direction diagrams of the scattered field are calculated. It is shown that a radially inhomogeneous coating can be modelled by a system of homogeneous elastic layers. For a </span>linear dependence of the inhomogeneity, the number of </span>homogeneous layers in the discretely-layered coating needed to ensure a prescribed accuracy of matching of the direction diagrams of bodies with a discretely layered coating to a continuously-inhomogeneous coating has been determined.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 6","pages":"Pages 480-485"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91717150","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: 7
Energy spectrum of turbulent velocity pulsations in a wide range of wave numbers (renorm-group approach) 大波数范围内湍流速度脉动的能谱(改革群法)
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-05-07 DOI: 10.1016/j.jappmathmech.2018.03.013
E.V. Teodorovich
{"title":"Energy spectrum of turbulent velocity pulsations in a wide range of wave numbers (renorm-group approach)","authors":"E.V. Teodorovich","doi":"10.1016/j.jappmathmech.2018.03.013","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.013","url":null,"abstract":"<div><p>Based on the concept of cascade mechanism of energy transfer over the wave-number spectrum and related to the locality property of intermodal interactions forming the energy spectrum, the unified formula for spectral energy density<span> is obtained that is valid in a wide range of wave numbers including both inertial and dissipation ranges<span>. The form of the spectrum is governed by three parameters, namely, a value of wave number chosen as the normalization point assigned to the edge of the domain of the stochasticity emergence due to the development of instability of large-scale flows and the turbulent energy production, the spectral energy flux through the boundary of energy production domain in the wave-number space (the energy pumping rate), and the fluid kinematic viscosity.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 6","pages":"Pages 450-454"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91672412","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: 2
The problem of the non-uniform sliding of an indenter over a viscoelastic foundation with applications to the calculation of the dynamics of a movable contact 粘弹性基础上压头的不均匀滑动问题及其在动接触动力学计算中的应用
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2017-10-11 DOI: 10.1016/j.jappmathmech.2017.08.010
I.A. Soldatenkov
{"title":"The problem of the non-uniform sliding of an indenter over a viscoelastic foundation with applications to the calculation of the dynamics of a movable contact","authors":"I.A. Soldatenkov","doi":"10.1016/j.jappmathmech.2017.08.010","DOIUrl":"10.1016/j.jappmathmech.2017.08.010","url":null,"abstract":"<div><p><span>The problem of the non-uniform sliding of an indenter over a viscoelastic foundation, whose deformation properties<span> are described by a simplified Kelvin model, is considered. An analytical solution is obtained, and it is established that it has a hereditary character, i.e., it depends on the past history of the interaction of the indenter with the foundation. The solution obtained is used to calculate the sliding dynamics of a massive body, i.e., the problem of braking of a massive indenter as it slides over a viscoelastic foundation and the problem of grasping a massive viscoelastic body by a pair of indenters sliding over its sides. The influence of the viscoelastic parameters and the shape of the indenter on the dynamic characteristics of the massive body is studied. In particular, it is shown that the type of dependence of the deformation friction force on the </span></span>sliding velocity has a significant influence on the braking mode of the indenter. The possibility of controlling the braking process is demonstrated.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 3","pages":"Pages 173-188"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.08.010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79533062","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: 3
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