Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

IF 4.2 Q2 NANOSCIENCE & NANOTECHNOLOGY
Soroush Sepehri, M. Mosavi Mashhadi, Mir Masoud Seyyed Fakhrabadi
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引用次数: 1

Abstract

The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.
考虑剪切变形的二维周期晶格中的波传播和方向性
剪切变形对周期性晶格波传播分析的影响通常被认为可以忽略不计。然而,这种假设并不总是正确的,特别是对于由较小宽高比的梁构成的晶格。因此,本文研究了剪切变形对波在不同拓扑结构的周期晶格中的传播的影响,并比较了它们的波衰减和定向性能。目前的实验限制使得研究人员更多地关注于微/纳米尺度晶格材料中垂直于周期平面方向的波传播,而对于宏观/中尺度晶格材料,既可以分析面内模式,也可以分析面外模式。本文考虑了六角形、三角形、正方形和菱形四种著名的拓扑结构,并研究了它们在周期平面和面外方向上的波传播。采用有限元法建立控制方程,采用布洛赫定理求解色散关系。为了研究剪切变形的影响,采用了Timoshenko和Euler-Bernoulli梁理论。结果表明,在波传播中加入剪切变形对波传播带图有软化作用,使频散分支向低频移动。它还可以揭示一些不考虑剪切变形而无法预测的带隙。
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来源期刊
CiteScore
6.00
自引率
1.70%
发文量
24
期刊介绍: Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems is a peer-reviewed scientific journal published since 2004 by SAGE Publications on behalf of the Institution of Mechanical Engineers. The journal focuses on research in the field of nanoengineering, nanoscience and nanotechnology and aims to publish high quality academic papers in this field. In addition, the journal is indexed in several reputable academic databases and abstracting services, including Scopus, Compendex, and CSA's Advanced Polymers Abstracts, Composites Industry Abstracts, and Earthquake Engineering Abstracts.
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