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The Ishlinskii oscillator model in the Keldysh shimmy problem Keldysh摆振问题中的Ishlinskii振子模型
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2016-07-07 DOI: 10.1016/j.jappmathmech.2016.06.003
N.P. Plakhtienko , B.M. Shifrin
{"title":"The Ishlinskii oscillator model in the Keldysh shimmy problem","authors":"N.P. Plakhtienko ,&nbsp;B.M. Shifrin","doi":"10.1016/j.jappmathmech.2016.06.003","DOIUrl":"10.1016/j.jappmathmech.2016.06.003","url":null,"abstract":"<div><p>A.Yu. Ishlinskii's idea concerning the correspondence between a ‘vibrating system at the threshold of stability and a hypothetical one-degree-of-freedom linear system’ is used. For the case of linear shimmy, procedures are proposed for constructing an oscillator model, checking its correspondence to a prescribed system, and using it to find the vibration frequencies and amplitudes. Within the framework of M.V. Keldysh's most simple calculation scheme, the shimmy of a towed, pliant pneumatic tyre is examined. The obtained laws of turning of the towing gear are compared with the results of numerical integration of the initial equations of motion. It is established that the oscillator model fits the Keldysh system adequately, at least if the length of the towing gear is no smaller than the radius of the pneumatic wheel.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 2","pages":"Pages 127-132"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.06.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84594778","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
A qualitative analysis of sets of trajectories of mechanical systems 机械系统轨迹集的定性分析
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2016-06-16 DOI: 10.1016/j.jappmathmech.2016.05.005
V.I. Slyn’ko
{"title":"A qualitative analysis of sets of trajectories of mechanical systems","authors":"V.I. Slyn’ko","doi":"10.1016/j.jappmathmech.2016.05.005","DOIUrl":"10.1016/j.jappmathmech.2016.05.005","url":null,"abstract":"<div><p><span>The evolution of geometric measures (volume, surface area) of sets of attainability of linear controlled </span>mechanical systems<span> with constant parameters is studied. Lyapunov's direct method, the comparison method, and theory of mixed volumes are used. Based on the general comparison theorem, estimates are obtained for the solutions of differential equations with a generalized Hukuhara derivative that describe the evolution of regions of attainability. For linear controlled systems with one degree of freedom, the maximum boundedness conditions are obtained for the area of the set of attainability. Examples of the application of the obtained results are given.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 1","pages":"Pages 24-32"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.05.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80652938","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
Mathematical model of the formation of a gas hydrate on the injection of gas into a stratum partially saturated with ice 向部分饱和冰层注入气体形成天然气水合物的数学模型
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2016-06-16 DOI: 10.1016/j.jappmathmech.2016.05.009
I.K. Gimaltdinov, M.K. Khasanov
{"title":"Mathematical model of the formation of a gas hydrate on the injection of gas into a stratum partially saturated with ice","authors":"I.K. Gimaltdinov,&nbsp;M.K. Khasanov","doi":"10.1016/j.jappmathmech.2016.05.009","DOIUrl":"10.1016/j.jappmathmech.2016.05.009","url":null,"abstract":"<div><p>The injection of a cold gas into a porous medium<span> saturated with gas and ice that is accompanied by the formation of a gas hydrate is studied theoretically. Self-similar solutions describing the distribution of the basic parameters in the stratum are constructed for an axisymmetric problem<span> with an extended region of phase transitions. The possible existence of four different types of solutions is indicated according to which, when cold gas is injected, it is possible that either a hydrate is formed from gas and ice on the front surface or there is hydrate formation from gas and ice in one extended region or hydrate formation both from gas and ice and gas and water in two extended regions or ice melts on the front surface and a hydrate is subsequently formed from gas and water on another front surface. Critical diagrams are constructed that distinguish the regions of existence of the different types of solutions.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 1","pages":"Pages 57-64"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.05.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86491266","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: 18
Vth International Conference on Topical Problems of Continuum Mechanics with a special session in honour of Alexander Manzhirov's 60th birthday 2–7 October 2017, Tsaghkadzor, Armenia 2017年10月2日至7日，第五届连续介质力学专题问题国际会议暨亚历山大·曼日罗夫60岁生日特别会议，亚美尼亚察格卡佐尔
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2017-08-14 DOI: 10.1016/j.jappmathmech.2017.07.009
{"title":"Vth International Conference on Topical Problems of Continuum Mechanics with a special session in honour of Alexander Manzhirov's 60th birthday 2–7 October 2017, Tsaghkadzor, Armenia","authors":"","doi":"10.1016/j.jappmathmech.2017.07.009","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2017.07.009","url":null,"abstract":"","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 6","pages":"Page 527"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137189300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Remarks on the paper by Sh. A. Mukhamediev, E. I. Ryzhak, and S. V. Sinyukhina “Stability of a two-layer system of inhomogeneous heavy barotropic fluids”, J. Appl. Math. Mech.: 2016, Vol. 80, No. 3, pp. 264–270 关于Sh. a . Mukhamediev, E. I. Ryzhak和S. V. Sinyukhina“非均质重正压流体双层系统的稳定性”论文的评论，J. apl。数学。动力机械。: 2016, Vol. 80, No. 3, pp. 264-270
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2016-11-09 DOI: 10.1016/j.jappmathmech.2016.08.003
A.G. Kulikovskii
{"title":"Remarks on the paper by Sh. A. Mukhamediev, E. I. Ryzhak, and S. V. Sinyukhina “Stability of a two-layer system of inhomogeneous heavy barotropic fluids”, J. Appl. Math. Mech.: 2016, Vol. 80, No. 3, pp. 264–270","authors":"A.G. Kulikovskii","doi":"10.1016/j.jappmathmech.2016.08.003","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2016.08.003","url":null,"abstract":"","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 3","pages":"Pages 271-272"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.08.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137392384","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
Stationary solutions in a model three-body problem 模型三体问题的固定解
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2016-11-05 DOI: 10.1016/j.jappmathmech.2016.09.007
A.A. Zlenko
{"title":"Stationary solutions in a model three-body problem","authors":"A.A. Zlenko","doi":"10.1016/j.jappmathmech.2016.09.007","DOIUrl":"10.1016/j.jappmathmech.2016.09.007","url":null,"abstract":"<div><p><span><span><span>Two visco-elastic bodies (deformable spheres) are considered which interact with each other and move in quasi-circular orbits in the attractive force field of a fixed centre – a heavy point mass. Their axes of rotation are perpendicular to their </span>orbital plane. Stationary solutions of the evolutionary equations of motion are found. In one particular case, they extend solutions of the restricted circular three-body problem corresponding to two </span>collinear libration points. All three bodies are located along a straight line. This implies synchronization of motion of the </span>barycentre<span> of the two visco-elastic bodies relative to the attracting centre with their orbital motion relative to the barycentre in a 1:1 resonance. The rotation of the two bodies relative to their own centres of mass takes place in such a way that the bodies “view” the attracting centre and each other from the same side, i.e., they are synchronized in a 1:1 resonance with their orbital motion. Instability of stationary solutions is analytically proven.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 4","pages":"Pages 324-332"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.09.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72738077","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 contact problem with the bulk application of intermolecular interaction forces: distinctive features of the subsurface stresses 大量应用分子间相互作用力的接触问题:地下应力的独特特征
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2017-07-08 DOI: 10.1016/j.jappmathmech.2017.06.009
I.A. Soldatenkov
{"title":"The contact problem with the bulk application of intermolecular interaction forces: distinctive features of the subsurface stresses","authors":"I.A. Soldatenkov","doi":"10.1016/j.jappmathmech.2017.06.009","DOIUrl":"10.1016/j.jappmathmech.2017.06.009","url":null,"abstract":"<div><p>The formulation of the contact problem is considered for the bulk application of intermolecular interaction forces between the contacting bodies as applied to the contact between an absolutely rigid body (an indentor) and an elastic half space. The subsurface stresses and, in particular, the shear stress intensity associated with the fracture of the material are analysed.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 6","pages":"Pages 518-526"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.06.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75857117","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
The motion of an elastoplastic medium in a circular tube heated due to boundary friction 由于边界摩擦而加热的圆管内弹塑性介质的运动
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2016-07-11 DOI: 10.1016/j.jappmathmech.2016.06.013
A.A. Burenin , L.V. Kovtanyuk , G.L. Panchenko
{"title":"The motion of an elastoplastic medium in a circular tube heated due to boundary friction","authors":"A.A. Burenin ,&nbsp;L.V. Kovtanyuk ,&nbsp;G.L. Panchenko","doi":"10.1016/j.jappmathmech.2016.06.013","DOIUrl":"10.1016/j.jappmathmech.2016.06.013","url":null,"abstract":"<div><p><span>The solution of a sequence of related problems in thermoelastoplasticity, concerning the origin and development of the flow of a medium in a cylindrical tube with a varying pressure drop and heating of the material due to friction at the tube wall with the subsequent flow deceleration when the load is slowly removed and the layer material cools off, is presented. The thermophysical and </span>deformation processes<span> are interconnected when the yield stress is temperature dependent. The conditions for the generation of a viscoplastic flow and the relations for the advancement of the elastoplastic boundaries through the layer are indicated, and the flow rates and both irreversible and reversible large deformations are calculated.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 2","pages":"Pages 190-197"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.06.013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81766924","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
Explicit form of the solution of the mixed problem for the seepage equation in a fractured-porous spatial layer with predominantly horizontal permeability 以水平渗透率为主的裂缝-孔隙空间层渗流方程混合问题的显式解
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2017-07-05 DOI: 10.1016/j.jappmathmech.2017.06.005
Kh.G. Umarov
{"title":"Explicit form of the solution of the mixed problem for the seepage equation in a fractured-porous spatial layer with predominantly horizontal permeability","authors":"Kh.G. Umarov","doi":"10.1016/j.jappmathmech.2017.06.005","DOIUrl":"10.1016/j.jappmathmech.2017.06.005","url":null,"abstract":"<div><p><span>For the Barenblatt–Zheltov–Kochina model representation of seepage of a fluid in a fractured-porous rock, an explicit form of the solution of the mixed problem in a fractured-porous spatial layer with predominantly horizontal permeability is found by reducing the problem to solution of the abstract mixed problem in a </span>Banach space.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 6","pages":"Pages 466-477"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.06.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75850671","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
Modelling the inhomogeneous coating of an elastic plate with optimum sound-reflecting properties 具有最佳声反射性能的弹性板的非均匀涂层建模
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 Epub Date: 2016-10-25 DOI: 10.1016/j.jappmathmech.2016.09.009
N.V. Larin, S.A. Skobel’tsyn, L.A. Tolokonnikov
{"title":"Modelling the inhomogeneous coating of an elastic plate with optimum sound-reflecting properties","authors":"N.V. Larin,&nbsp;S.A. Skobel’tsyn,&nbsp;L.A. Tolokonnikov","doi":"10.1016/j.jappmathmech.2016.09.009","DOIUrl":"10.1016/j.jappmathmech.2016.09.009","url":null,"abstract":"<div><p>The problem of determining the laws governing the inhomogeneity of the coating of a plane elastic plate that ensure the least reflection with a given angle of incidence of a plane sound wave is considered. On the basis of the direct problem solution, a functional representing the intensity of reflection is constructed, and an algorithm for its minimisation is proposed. Analytical expressions describing the mechanical parameters of the inhomogeneous coating are obtained.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 4","pages":"Pages 339-344"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.09.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88635635","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
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