Low-frequency band gaps in one-dimensional thin phononic crystal plate with periodic stubbed surface

Yao, Yuanwei; Hou, Zhipeng; Wu, Fugen; Zhang, Xin

doi:10.1016/j.physb.2011.03.043

Cited by 24 publications

(9 citation statements)

References 13 publications

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“…This result has been applied to filtering or multiplexing [101]. The characteristics of the band structure and wave transmission when the stubs are grafted to the tube in a single side [102][103][104], double symmetric sides [105][106][107][108], and asymmetric sides [109] were theoretically and experimentally investigated.…”

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confidence: 99%

Physics of surface vibrational resonances: pillared phononic crystals, metamaterials, and metasurfaces

et al. 2021

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The introduction of engineered resonance phenomena on surfaces has opened a new frontier in surface science and technology. Pillared phononic crystals, metamaterials, and metasurfaces are an emerging class of artificial structured materials, featuring surfaces, that consist of pillars-or branching substructures-standing on a substrate or a plate. A pillared phononic crystal exhibits Bragg band gaps while a pillared metamaterial may feature both Bragg gaps and local-resonance hybridization gaps. These two band-gap phenomena, along with other unique wave dispersion characteristics, have been exploited for a variety of applications spanning a range of length scales and covering multipe disciplines in applied physics and engineering. The placement of pillars on a semi-infinite surface has similarly provided new avenues for the control and manipulation of wave propagation, including Rayleigh and Love waves along the surface of substrates, as well as Lamb waves in plates-for frequencies ranging from Hz to several GHz. Even a finite placement of pillars along specific directions on a surface has been shown to offer unique functionality, such as steering a wavefront in the subwavelength regime. At the nanoscale, pillared membranes have been investigated and it was shown that atomic-scale resonances-stemming from the nanopillars-alter the fundamental nature of conductive thermal transport by reducing the group velocities and generating mode localization across the entire spectrum well into the THz regime. In this article, we first overview the history and development of pillared materials, then provide a detailed synopsis of a selection of key research topics that involve the utilization of pillars in different contexts. The following sections present a review of different configurations, properties, and 2 characteristics, namely: (i) fundamental vibrational and propagation properties of pillared plates; (ii) metamaterial phenomena in pillared plates including the opening of low and wide hybridization band gaps as well as super-resolution focusing; (iii) pillared metasurfaces and their wave steering functions;(iv) topologically protected phononic edge states in pillared plates; and (v) nanophononic metamaterials in the form of pillared membranes exhibiting exceptionally low in-plane thermal conductivity. Finally, we conclude by providing a short summary on the salient properties of pillared materials and structures and outlining some perspectives on the state of the field and its promise for further future development.

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Physics of surface vibrational resonances: pillared phononic crystals, metamaterials, and metasurfaces

et al. 2021

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“…among other configurations. In one-dimensional (1D) structures, among the metamaterial configurations investigated are three-phase rods, 18 beams with resonating rings, 19,20 sandwich beams with internal mass-spring resonators, 21 beams with side stubs, 22,23 chains of beads with cylindrical resonators, 24 and beams with small masses suspended on membranes. 25 The band-gap formation mechanism in this class of 1D systems was studied analytically by Xiao et al in the context of mass resonators attached to strings, 26 rods 27 and beams.…”

Section: A Elastic Metamaterialsmentioning

confidence: 99%

Dispersion characteristics of a nonlinear elastic metamaterial

2014

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We study wave dispersion in a one-dimensional nonlinear elastic metamaterial consisting of a thin rod with periodically attached local resonators. Our model is based on an exact finite-strain dispersion relation for a homogeneous solid, utilized in conjunction with the standard transfer matrix method for a periodic medium. The nonlinearity considered stems from large elastic deformation in the thin rod, whereas the metamaterial behavior is associated with the dynamics of the local resonators. We derive an approximate dispersion relation for this system and provide an analytical prediction of band-gap characteristics. The results demonstrate the effect of the nonlinearity on the characteristics of the band structure, including the size, location, and character of the band gaps. For example, large deformation alone may cause a pair of isolated Bragg-scattering and local-resonance band gaps to coalesce. We show that for a wave amplitude on the order of one-eighth of the unit cell size, the effect of the nonlinearity in the structure considered is no longer negligible when the unit-cell size is one-fourteenth of the wavelength or larger.

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“…Zhao et al [3] studied the peculiar transmission peaks of PnCs in both theoretical analysis and experimental observation. Moreover, band gaps in PnCs with one [4][5][6][7], two [8][9][10][11][12][13][14] or three [15][16][17][18] dimensional lattices were widely studied. Along with the mature of ABG determination in given PnCs, PnC optimization according to application demands becomes essential.…”

Section: Introductionmentioning

confidence: 99%

“…(5) under the complex boundary condition of Eq(5). The model built in COMSOL is saved as a MATLAB-compatible '.m' file.The unit cell is meshed by triangular Lagrange quadratic elements provided by the code.…”

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Follow-up optimized phononic band structure design based on reserved inclusions

Wang

Liu

Wang

2019

Physica B: Condensed Matter

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For functional demands, inclusions are always reserved beforehand in a structural design. In this paper, a follow-up optimized phononic band structure design is performed based on a 2D structure with reserved inclusions but no absolute band gaps for the purpose to simultaneously achieve acoustic abatement except for functional demands. Firstly, the strategy to optimize the band structure based on bidirectional evolutionary structural optimization algorithm is proposed. Then the effects of geometrical or physical parameters on the final optimization results are discussed. Numerical results show that there is a material gravitation phenomenon around the inclusions in the topological optimization. Factors affecting the material gravitation are discussed in details. This work will lead an important guidance in the multifunctional design of multi-phase phononic crystals.

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Low-frequency band gaps in one-dimensional thin phononic crystal plate with periodic stubbed surface

Cited by 24 publications

References 13 publications

Physics of surface vibrational resonances: pillared phononic crystals, metamaterials, and metasurfaces

Physics of surface vibrational resonances: pillared phononic crystals, metamaterials, and metasurfaces

Dispersion characteristics of a nonlinear elastic metamaterial

Follow-up optimized phononic band structure design based on reserved inclusions

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