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Pmm Journal of Applied Mathematics and Mechanics最新文献

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Matrix method of constructing the differential equations of motion of an exoskeleton and its control 构造外骨骼运动微分方程及其控制的矩阵法
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.002
A.V. Borisov , G.M. Rozenblat
{"title":"Matrix method of constructing the differential equations of motion of an exoskeleton and its control","authors":"A.V. Borisov ,&nbsp;G.M. Rozenblat","doi":"10.1016/j.jappmathmech.2018.03.002","DOIUrl":"10.1016/j.jappmathmech.2018.03.002","url":null,"abstract":"<div><p><span>Two mathematical models of rods of variable length from which an exoskeleton can be created, providing comfortable movement of a human in it owing to duplication of the properties of a motion-support apparatus, are considered. Their structure is elucidated on the basis of an analysis of the differential equations of motion, allowing for representing them in vector-matrix form. General regularities of the construction of the matrix elements entering into the </span>system of differential equations of motion are established and generalizing formulae for the matrix elements are obtained. A new matrix method of constructing the differential equations of motion is presented and illustrated by a specific example. This system of equations is solved numerically. The possibility of reinforcing the control actions for control of the exoskeleton motion with a human inside it is considered.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 351-359"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87247554","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: 16
The approach problem of a nonlinear controlled system in a finite time interval 有限时间区间内非线性控制系统的逼近问题
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.08.005
A.R. Matviychuk, V.I. Ukhobotov, A.V. Ushakov, V.N. Ushakov
{"title":"The approach problem of a nonlinear controlled system in a finite time interval","authors":"A.R. Matviychuk,&nbsp;V.I. Ukhobotov,&nbsp;A.V. Ushakov,&nbsp;V.N. Ushakov","doi":"10.1016/j.jappmathmech.2017.08.005","DOIUrl":"10.1016/j.jappmathmech.2017.08.005","url":null,"abstract":"<div><p>A nonlinear controlled system in Euclidean space, which is specified in a finite time interval, is considered. The approach problem of a controlled system with a target set in a finite time interval is studied. An algorithm for an approximate calculation of the solution of the problem is presented. An illustrative example of a “flywheel–pendulum” controlled mechanical system is considered.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 2","pages":"Pages 114-128"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.08.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76867444","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
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 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
The angular motion of oceanic vortex formations 海洋涡旋形成的角运动
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.007
E.K. Lavrovskii, V.V. Fominykh
{"title":"The angular motion of oceanic vortex formations","authors":"E.K. Lavrovskii,&nbsp;V.V. Fominykh","doi":"10.1016/j.jappmathmech.2018.03.007","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.007","url":null,"abstract":"<div><p><span>Within the framework of the rigid body hypothesis, the influence of external torques acting on a rotating water lens in a stratified ocean is examined and a hypothesis about the angular motion of objects of such kind is constructed. The structure of the external torques acting on the lens is investigated and their magnitudes and influence on the overall picture of the motion of the lens about its centre of mass are estimated. It is shown that the hydrostatic buoyancy torque is the most important of such torques, it being orders of magnitude greater than the Coriolis torque and the torque due to virtual masses, and also the gravitational torque and other torques. The </span>friction torque can promote stabilization of the angular motion and lead to the appearance of a steady regime. The results obtained are in agreement with the observed motion of oceanic formations.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 390-394"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91724953","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
Limit periodic motions in systems with after-effect in a critical case* 临界情况下具有后效应系统的周期运动极限*
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.001
V.S. Sergeev
{"title":"Limit periodic motions in systems with after-effect in a critical case*","authors":"V.S. Sergeev","doi":"10.1016/j.jappmathmech.2018.03.001","DOIUrl":"10.1016/j.jappmathmech.2018.03.001","url":null,"abstract":"<div><p>Systems with after-effect are considered, whose states are described by Volterra integro-differential equations. The critical case of one zero root of the characteristic equation is investigated (where all the other roots have negative real parts) along with the question of the existence in this case of limit periodic motions of the system, i.e., motions which tend exponentially to periodic regimes with unbounded increase of time. A time-dependent, small, piecewise-continuous limit periodic perturbation, generated by external factors, is present in the system. It is shown that in the system under the perturbation, limit periodic motions arise that are represented by power series in fractional powers of a small parameter characterizing the perturbation magnitude. As an example, rotational limit periodic oscillations of a solid plate in an air flow are considered with time dependence of the flow about the plate taken into account by introducing integral terms into the aerodynamic torque.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 343-350"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72545525","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
The stability of the motion of a non-axisymmetric body in a resistive medium 非轴对称物体在电阻介质中运动的稳定性
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.014
K. Yu. Osipenko
{"title":"The stability of the motion of a non-axisymmetric body in a resistive medium","authors":"K. Yu. Osipenko","doi":"10.1016/j.jappmathmech.2018.03.014","DOIUrl":"10.1016/j.jappmathmech.2018.03.014","url":null,"abstract":"<div><p><span>A mathematical model of the plane motion of a non-axisymmetric body in a resistive medium is constructed using the local interaction method. Criteria for the stability of </span>rectilinear<span> motion are obtained in a general form in the case of a frozen axial velocity<span>. The stability of the motion of a regular triangular pyramid is investigated in detail when a constant friction and pressure, specified using an empirical Poncelet formula in the form of a sum of inertial and strength terms, acts on its lateral surface. The stabilities of a pyramid and a cone are compared. The effect of deceleration on the stability of the rectilinear motion is considered.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 6","pages":"Pages 455-462"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72410025","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
Steady rotations of a satellite with internal elastic and dissipative forces 具有内部弹性和耗散力的卫星的稳定旋转
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/J.JAPPMATHMECH.2018.03.011
N. Amelkin, V. Kholoshchak
{"title":"Steady rotations of a satellite with internal elastic and dissipative forces","authors":"N. Amelkin, V. Kholoshchak","doi":"10.1016/J.JAPPMATHMECH.2018.03.011","DOIUrl":"https://doi.org/10.1016/J.JAPPMATHMECH.2018.03.011","url":null,"abstract":"","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"13 1","pages":"431-441"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74297668","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: 4
Cavitation flow of an ideal incompressible fluid in the electrochemical machining of metals 金属电解加工中理想不可压缩流体的空化流
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.07.004
N.M. Minazetdinov
{"title":"Cavitation flow of an ideal incompressible fluid in the electrochemical machining of metals","authors":"N.M. Minazetdinov","doi":"10.1016/j.jappmathmech.2017.07.004","DOIUrl":"10.1016/j.jappmathmech.2017.07.004","url":null,"abstract":"<div><p>The limiting simplest model of the non-linear two-dimensional problem of the electrochemical machining of metals taking account of the attached cavitation<span> is constructed on the basis of a model of an ideal electrochemical shaping process and the theory of ideal incompressible fluid jets. A solution is obtained related to the determination of the steady shape of the surface of the component (anode) taking account of the cavity formed in the machining on the cathode tool boundary. The results of the calculations show that the model reflects the qualitative effects related to the effect of the added cavity on the shape of the machined component.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 29-35"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77540817","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
Theory of piezoelectric laminated plates as an asymptotic approximation of the three-dimensional problem 压电层合板理论作为三维问题的渐近逼近
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.07.006
I.D. Kochetkov, N.N. Rogacheva
{"title":"Theory of piezoelectric laminated plates as an asymptotic approximation of the three-dimensional problem","authors":"I.D. Kochetkov,&nbsp;N.N. Rogacheva","doi":"10.1016/j.jappmathmech.2017.07.006","DOIUrl":"10.1016/j.jappmathmech.2017.07.006","url":null,"abstract":"<div><p><span>A theory of laminated plates, whose central plane coincides with the symmetry plane of the plate, has been constructed by the </span>asymptotic method of reducing the three-dimensional equations of piezoelectricity to the two-dimensional equations of piezoelectric plates without the use of any hypotheses. The plate contains both elastic and piezoelectric layers. The constructed theory is compared with the theories of other authors. As an example, a numerical calculation has been carried out of the piezoelectric state of a circular three-layer plate performing induced harmonic vibrations.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 52-65"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85533647","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
Internal gravity waves excited by a pulsating perturbation source 由脉动扰动源激发的内部重力波
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.006
V.V. Bulatov, Yu.V. Vladimirov
{"title":"Internal gravity waves excited by a pulsating perturbation source","authors":"V.V. Bulatov,&nbsp;Yu.V. Vladimirov","doi":"10.1016/j.jappmathmech.2018.03.006","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.006","url":null,"abstract":"<div><p><span>The problem of an internal gravity wave field from a pulsating point source of perturbations in the flow of a stratified medium of finite depth with horizontal velocity of the source </span><em>V</em><span> less than the maximum value of the group velocity of the internal gravity waves </span><em>c</em> is considered, unlike to the previously considered case <em>V</em> <!-->&gt;<!--> <em>c</em><span>. Constructed asymptotic solutions make it possible to describe the amplitude-phase characteristics of individual modes comprising the full field of internal gravity waves. The excited waves consist of waves of two types: ring-like waves and wedge-shaped waves. Features of the mode structure of the excited fields are considered as functions of the parameters of the stratified medium and the characteristics of the perturbation source.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 384-389"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91724952","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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