Abstract
This study is devoted to the analysis of the band structures of the anti-plane transverse wave (SH wave) in nanoscale layered metamaterial structures. Attention is restricted to normal incidence of waves. The localization factor is introduced to characterize the band structures. The general transfer matrix method based on the nonlocal elastic continuum theory is employed to calculate the localization factor. Based on the analysis of band structures, the influences of random disorder of the internal characteristic length and the external thickness of each sub-layer, the aperiodic arrangements, the location of different material components, the ratio of mass density, the ratio of the transverse wave velocity, the ratio of the internal characteristic length or the external thickness of each sub-layer on the band structures, the cut-off frequency, the peak points and the dense band zones are investigated and discussed in detail, which can provide some new thoughts for the designs and applications of the nanoscale wave devices.
Highlights
The metamaterials, phononic crystals (PCs) (Kushwaha et al, 1993), have been studied intensely over the past 2 decades due to their potential capability of controlling and tuning the propagation of acoustic/elastic waves
The band structures and localization properties of the anti-plane elastic waves propagating normally in nanoscale layered structures are studied by the general transfer matrix method
It can be seen that with the exchange of material components, the distance between the two peak points becomes narrower, and the two peak points and the first distinct band gap move to the low frequency zone
Summary
The metamaterials, phononic crystals (PCs) (Kushwaha et al, 1993), have been studied intensely over the past 2 decades due to their potential capability of controlling and tuning the propagation of acoustic/elastic waves. The influences of random disorder of the internal characteristic length and the external thickness of each sub-layer, the aperiodic arrangements, the location of different material components, the ratio of the mass density, the ratio of the transverse wave velocity, the ratio of the internal characteristic length or the external thickness of each sub-layer on the band structures, the cut-off frequency, the peak points and the DBZs have not been investigated, which requires a detailed study of these problems. A detailed parametric study is conducted to investigate the influences of random disorder of the internal characteristic length and the external thickness of each sub-layer, the aperiodic arrangements, the location of different components, the ratio of the mass density, the ratio of the transverse wave velocity, the ratio of the internal characteristic length or the external thickness of each sub-layer on the band structures, the cut-off frequency, the peak points and the DBZs. The paper is structured as follows: Section 2 introduces the nonlocal elastic continuum theory.
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