Knowledge Management System of Institue of Mechanics, CAS
| On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model | |
Wang, Binying1; Liu, Jinxing1 ; Soh, A. K.2; Liang NG(梁乃刚)3
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| Corresponding Author | Liu, Jinxing(jxliu@mails.ucas.ac.cn) |
| Source Publication | APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
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| 2022 | |
| Volume | 43Issue:1Pages:1-20 |
| ISSN | 0253-4827 |
| Abstract | We have proposed an "exact" strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing. Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice, resulting in a novel SG model. For various kinds of diatomic lattices, the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone, manifesting the robustness of the present model. Based on this SG model, we have conducted the following discussions. (I) Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials, which is very helpful for the design of metamaterials. (II) The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted. Without doing so, the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy. The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone. (III) The effects of the nonlocal interactions are analyzed. The nonlocal interactions reduce the workable range of the well-known long-wave approximation, causing more local extrema in the dispersive diagrams. The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing, i.e., when the long-wave approximation is no longer valid. For the convenience of band gap designs, we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width. |
| Keyword | band gap diatomic lattice strain gradient (SG) continuum dispersion Taylor expansion Brillouin zone nonlocal interaction O33 |
| DOI | 10.1007/s10483-021-2795-5 |
| Indexed By | SCI ; EI ; CSCD |
| Language | 英语 |
| WOS ID | WOS:000737924400001 |
| WOS Keyword | WAVE-PROPAGATION ; CONTINUUM MODEL ; VIBRATION ; MECHANISM |
| WOS Research Area | Mathematics ; Mechanics |
| WOS Subject | Mathematics, Applied ; Mechanics |
| Funding Project | National Natural Science Foundation of China[11972174] ; National Natural Science Foundation of China[11672119] |
| Funding Organization | National Natural Science Foundation of China |
| Classification | 一类 |
| Ranking | 3+ |
| Contributor | Liu, Jinxing |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/88273 |
| Collection | 职能与支撑部门 |
| Affiliation | 1.Jiangsu Univ, Fac Civil Engn & Mech, Zhenjiang 212203, Jiangsu, Peoples R China; 2.Monash Univ Malaysia, Sch Engn, Selangor Darul Ehsan 47500, Malaysia; 3.Chinese Acad Sci, Inst Mech, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Wang, Binying,Liu, Jinxing,Soh, A. K.,et al. On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model[J]. APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION,2022,43,1,:1-20. |
| APA | Wang, Binying,Liu, Jinxing,Soh, A. K.,&梁乃刚.(2022).On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model.APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION,43(1),1-20. |
| MLA | Wang, Binying,et al."On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model".APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION 43.1(2022):1-20. |
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| Jp2022FA578_2022_On （1353KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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