{"title":"承载运动子系统的柔性结构内力的跳跃不连续","authors":"Bingen Yang, Hao Gao","doi":"10.1115/1.4062628","DOIUrl":null,"url":null,"abstract":"Abstract Combined systems, which are flexible structures carrying moving subsystems, are seen in various applications. Due to structure–subsystem interactions, the structure in a combined system encounters jump discontinuities in its internal forces (such as the bending moment and shear force of a beam). Accurate estimation of such jump discontinuities is important to the performance, safety, and longevity of a combined system. Because of the time-varying nature and complexity of structure–subsystem interactions, conventional series solution methods experience slow convergence, and the Gibbs phenomenon in computation and the improved series expansion methods are limited to certain proportionally damped continua under moving forces and moving oscillators. In this paper, a novel modified series expansion method (MSEM) is proposed to resolve the aforementioned issues with the existing series solution methods. Through the introduction of a jump influence function, the proposed method produces fast-convergent series solutions and accurately predicts the jump discontinuities without the Gibbs phenomenon. The MSEM is applicable to structures with nonproportional damping and subject to arbitrary boundary conditions, and it can easily manage general M-DOF moving subsystems having multiple contact points with a supporting structure. As an important result of this investigation, a mathematical proof of the convergence of the MSEM-based solutions is given for the first time. Additionally, two numerical examples are presented to demonstrate the accuracy, efficiency, and versatility of the proposed MSEM in modeling and analysis of combined systems.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"80 1","pages":"0"},"PeriodicalIF":2.6000,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Jump Discontinuities in Internal Forces of Flexible Structures Carrying Moving Subsystems\",\"authors\":\"Bingen Yang, Hao Gao\",\"doi\":\"10.1115/1.4062628\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Combined systems, which are flexible structures carrying moving subsystems, are seen in various applications. Due to structure–subsystem interactions, the structure in a combined system encounters jump discontinuities in its internal forces (such as the bending moment and shear force of a beam). Accurate estimation of such jump discontinuities is important to the performance, safety, and longevity of a combined system. Because of the time-varying nature and complexity of structure–subsystem interactions, conventional series solution methods experience slow convergence, and the Gibbs phenomenon in computation and the improved series expansion methods are limited to certain proportionally damped continua under moving forces and moving oscillators. In this paper, a novel modified series expansion method (MSEM) is proposed to resolve the aforementioned issues with the existing series solution methods. Through the introduction of a jump influence function, the proposed method produces fast-convergent series solutions and accurately predicts the jump discontinuities without the Gibbs phenomenon. The MSEM is applicable to structures with nonproportional damping and subject to arbitrary boundary conditions, and it can easily manage general M-DOF moving subsystems having multiple contact points with a supporting structure. As an important result of this investigation, a mathematical proof of the convergence of the MSEM-based solutions is given for the first time. Additionally, two numerical examples are presented to demonstrate the accuracy, efficiency, and versatility of the proposed MSEM in modeling and analysis of combined systems.\",\"PeriodicalId\":54880,\"journal\":{\"name\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"volume\":\"80 1\",\"pages\":\"0\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4062628\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics-Transactions of the Asme","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4062628","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
On Jump Discontinuities in Internal Forces of Flexible Structures Carrying Moving Subsystems
Abstract Combined systems, which are flexible structures carrying moving subsystems, are seen in various applications. Due to structure–subsystem interactions, the structure in a combined system encounters jump discontinuities in its internal forces (such as the bending moment and shear force of a beam). Accurate estimation of such jump discontinuities is important to the performance, safety, and longevity of a combined system. Because of the time-varying nature and complexity of structure–subsystem interactions, conventional series solution methods experience slow convergence, and the Gibbs phenomenon in computation and the improved series expansion methods are limited to certain proportionally damped continua under moving forces and moving oscillators. In this paper, a novel modified series expansion method (MSEM) is proposed to resolve the aforementioned issues with the existing series solution methods. Through the introduction of a jump influence function, the proposed method produces fast-convergent series solutions and accurately predicts the jump discontinuities without the Gibbs phenomenon. The MSEM is applicable to structures with nonproportional damping and subject to arbitrary boundary conditions, and it can easily manage general M-DOF moving subsystems having multiple contact points with a supporting structure. As an important result of this investigation, a mathematical proof of the convergence of the MSEM-based solutions is given for the first time. Additionally, two numerical examples are presented to demonstrate the accuracy, efficiency, and versatility of the proposed MSEM in modeling and analysis of combined systems.
期刊介绍:
All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation