On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

doi:10.1007/s10483-021-2795-5

	On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model
	Wang, Binying 3; Liu, Jinxing 3; Soh, A. K.2; Liang NG(梁乃刚)1
刊名	APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
	2022
卷号	43 期号:1 页码:1-20
关键词	band gap diatomic lattice strain gradient (SG) continuum dispersion Taylor expansion Brillouin zone nonlocal interaction O33
ISSN号	0253-4827
DOI	10.1007/s10483-021-2795-5
通讯作者	Liu, Jinxing(jxliu@mails.ucas.ac.cn)
英文摘要	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continuum theory when the wavelength gets close to the lattice spacing, i.e., when the long-wave approximation is no longer valid.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.
分类号	一类
资助项目	National Natural Science Foundation of China[11972174] ; National Natural Science Foundation of China[11672119]
WOS关键词	WAVE-PROPAGATION ; CONTINUUM MODEL ; VIBRATION ; MECHANISM
WOS研究方向	Mathematics ; Mechanics
语种	英语
WOS记录号	WOS:000737924400001
资助机构	National Natural Science Foundation of China
其他责任者	Liu, Jinxing
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/88272]
专题	力学研究所_职能与支撑部门
作者单位	1.Chinese Acad Sci, Inst Mech, Beijing 100190, Peoples R China 2.Monash Univ Malaysia, Sch Engn, Selangor Darul Ehsan 47500, Malaysia; 3.Jiangsu Univ, Fac Civil Engn & Mech, Zhenjiang 212203, Jiangsu, Peoples R China;
推荐引用方式 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.