KMS Of Academy of mathematics and systems sciences, CAS
Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations | |
Li, Z. H.1,2; Ma, Q.1,2; Cui, J. Z.3 | |
2017-04-15 | |
Source Publication | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING |
ISSN | 0045-7825 |
Volume | 317Pages:1068-1101 |
Abstract | A new modal analysis method with second-order two-scale (SOTS) asymptotic expansion is presented for axisymmetric and spherical symmetric structures. The symmetric structures considered are periodically distributed with homogeneous and isotropic constituent materials. By the asymptotic expansion of the eigenfunctions, the homogenized modal equations, the effective materials coefficients, the first-and second-order correctors are obtained. The derived homogenized constitutive relationships are the same as the ones which serve to homogenize the corresponding static problems. The eigenvalues are also expanded to the second-order terms and using the so called "corrector equation", the correctors of the eigenvalues are expressed in terms of the first-and second-order correctors of the eigenfunctions. The anisotropic materials are obtained by homogenization with different properties in the circumferential direction. Especially for the two-dimensional axisymmetric layered structure, the one-dimensional plane axisymmetric and spherical symmetric structures, the homogenized eigenfunctions and eigenvalues, as well as their corresponding correctors are all solved analytically. The finite element algorithm is established, three typical numerical experiments are carried out and the necessity of the second-order correctors is discussed. Based on the numerical results, it is validated that the SOTS asymptotic expansion homogenization method is effective to identify the eigenvalues of the axisymmetric and spherical symmetric structures with periodic configurations and the original eigenfunctions with periodic oscillation can be reproduced by adding the correctors to the homogenized eigenfunctions. (C) 2017 The Authors. Published by Elsevier B.V. |
Keyword | Asymptotic expansion homogenization method SOTS finite element algorithm Modal analysis Eigenvalue problem Axisymmetric and spherical symmetric structure Periodic configuration |
DOI | 10.1016/j.cma.2017.01.013 |
Language | 英语 |
Funding Project | National Key Basic Research and Development Program[2014CB744100] ; National Nature Science Foundation of China[11325212] ; National Nature Science Foundation of China[91530319] ; China Postdoctoral Science Foundation[2014M562616] ; China Postdoctoral Science Foundation[2016T91019] |
WOS Research Area | Engineering ; Mathematics ; Mechanics |
WOS Subject | Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics |
WOS ID | WOS:000398373500043 |
Publisher | ELSEVIER SCIENCE SA |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/25106 |
Collection | 计算数学与科学工程计算研究所 |
Corresponding Author | Li, Z. H. |
Affiliation | 1.China Aerodynam Res & Dev Ctr, Hyperveloc Aerodynam Inst, Mianyang 621000, Peoples R China 2.BUAA, Natl Lab Computat Fluid Dynam, Beijing 100191, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China |
Recommended Citation GB/T 7714 | Li, Z. H.,Ma, Q.,Cui, J. Z.. Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2017,317:1068-1101. |
APA | Li, Z. H.,Ma, Q.,&Cui, J. Z..(2017).Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,317,1068-1101. |
MLA | Li, Z. H.,et al."Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 317(2017):1068-1101. |
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