KMS Of Academy of mathematics and systems sciences, CAS
| A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam | |
| Liu, Jiankang1; Guo, Bao-Zhu2,3,4 | |
| 2019-12-01 | |
| Source Publication | SYSTEMS & CONTROL LETTERS
 |
| ISSN | 0167-6911 |
| Volume | 134Pages:10 |
| Abstract | In this paper, a novel space semi-discretized numerical scheme which is based on finite volume method is proposed for approximation of uniformly exponential decay of Euler-Bernoulli beam system, which turns out to be an alternative of finite-difference scheme from order reduction point of view. The new scheme is constructed on equidistant grid points without using any numerical viscosity terms. The uniformly exponential decay is proved by the Lyapunov function method and the energy multiplier technique. With construction of a new gradient recovery function, the numerical solution is proved to be convergent to the (weak) solution of the original continuous system. Compared with the existing literature, the proposed approach has potentially achieved the following objectives: a) It removes the introduction of the numerical viscosity term to achieve uniform convergence; b) It can deal with any type of boundary conditions without help of the spectral analysis which is limited only for some special boundary conditions; c) the convergence proof is simplified significantly with the similar techniques in dealing with the continuous counterpart. (C) 2019 Elsevier B.V. All rights reserved. |
| Keyword | Beam equation Finite volume method Finite difference method Exponential stability Uniform approximation |
| DOI | 10.1016/j.sysconle.2019.104518 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11901365] ; National Natural Science Foundation of China[61873260] ; Project of Department of Education of Guangdong Province[2017KZDXM087] |
| WOS Research Area | Automation & Control Systems ; Operations Research & Management Science |
| WOS Subject | Automation & Control Systems ; Operations Research & Management Science |
| WOS ID | WOS:000501653800003 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50403 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Liu, Jiankang |
| Affiliation | 1.Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China 2.North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China 3.Acad Sinica, Key Lab Syst & Control, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Univ Witwatersrand, Sch Comp Sci & Appl Math, ZA-2050 Johannesburg, South Africa |
| Recommended Citation GB/T 7714 | Liu, Jiankang,Guo, Bao-Zhu. A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam[J]. SYSTEMS & CONTROL LETTERS,2019,134:10. |
| APA | Liu, Jiankang,&Guo, Bao-Zhu.(2019).A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam.SYSTEMS & CONTROL LETTERS,134,10. |
| MLA | Liu, Jiankang,et al."A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam".SYSTEMS & CONTROL LETTERS 134(2019):10. |
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