{"title":"单轴拉伸-压缩后,异模态弹性半空间中的平面应变波在其边界强制停止阶段的相互作用","authors":"O. V. Dudko, A. A. Lapteva, V. E. Ragozina","doi":"10.1134/S1990478923040038","DOIUrl":null,"url":null,"abstract":"<p> The evolution of the wave pattern in a multimodulus elastic half-space with a boundary\nmoving in nonstationary uniaxial piecewise linear “tension–compression–stop” mode is studied.\nThe solution of the boundary value problem includes all cases of interaction between plane\none-dimensional strain waves, including reflected weak-intensity fronts. A number of new features\nof one-dimensional elastic deformation dynamics in a multimodulus medium are revealed, some of\nwhich (e.g., the appearance of a reflected shock wave at a distance from the loaded boundary,\ncyclic transitions of a narrow moving zone from a compressed to rigid state and back, and a\nstepwise decrease in the tensile strain level in the near-boundary zone after the boundary is\nstopped) can be obtained with a given boundary loading only taking into account reflection\neffects.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"710 - 723"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Interaction of Plane Strain Waves in a Heteromodular Elastic Half-Space at the Stage of Forced Stopping of Its Boundary after Uniaxial Tension–Compression\",\"authors\":\"O. V. Dudko, A. A. Lapteva, V. E. Ragozina\",\"doi\":\"10.1134/S1990478923040038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> The evolution of the wave pattern in a multimodulus elastic half-space with a boundary\\nmoving in nonstationary uniaxial piecewise linear “tension–compression–stop” mode is studied.\\nThe solution of the boundary value problem includes all cases of interaction between plane\\none-dimensional strain waves, including reflected weak-intensity fronts. A number of new features\\nof one-dimensional elastic deformation dynamics in a multimodulus medium are revealed, some of\\nwhich (e.g., the appearance of a reflected shock wave at a distance from the loaded boundary,\\ncyclic transitions of a narrow moving zone from a compressed to rigid state and back, and a\\nstepwise decrease in the tensile strain level in the near-boundary zone after the boundary is\\nstopped) can be obtained with a given boundary loading only taking into account reflection\\neffects.\\n</p>\",\"PeriodicalId\":607,\"journal\":{\"name\":\"Journal of Applied and Industrial Mathematics\",\"volume\":\"17 4\",\"pages\":\"710 - 723\"},\"PeriodicalIF\":0.5800,\"publicationDate\":\"2024-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1990478923040038\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923040038","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
Interaction of Plane Strain Waves in a Heteromodular Elastic Half-Space at the Stage of Forced Stopping of Its Boundary after Uniaxial Tension–Compression
The evolution of the wave pattern in a multimodulus elastic half-space with a boundary
moving in nonstationary uniaxial piecewise linear “tension–compression–stop” mode is studied.
The solution of the boundary value problem includes all cases of interaction between plane
one-dimensional strain waves, including reflected weak-intensity fronts. A number of new features
of one-dimensional elastic deformation dynamics in a multimodulus medium are revealed, some of
which (e.g., the appearance of a reflected shock wave at a distance from the loaded boundary,
cyclic transitions of a narrow moving zone from a compressed to rigid state and back, and a
stepwise decrease in the tensile strain level in the near-boundary zone after the boundary is
stopped) can be obtained with a given boundary loading only taking into account reflection
effects.
期刊介绍:
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.