Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators

In this paper, we present a design of locally resonant (LR) beams using periodic arrays of beam-like resonators (or beam-like vibration absorbers) attached to a thin homogeneous beam. The main purpose of this work is twofold: (i) providing a theoretical characterization of the proposed LR beams, including the band gap behavior of infinite systems and the vibration transmittance of finite structures, and (ii) providing experimental evidence of the associated band gap properties, especially the coexistence of LR and Bragg band gaps, and their evolution with tuned local resonance. For the first purpose, an analytical method based on the spectral element formulations is presented, and then an in-depth numerical study is performed to examine the band gap effects. In particular, explicit formulas are provided to enable an exact calculation of band gaps and an approximate prediction of band gap edges. For the second purpose, we fabricate several LR beam specimens by mounting 16 equally spaced resonators onto a free-free host beam. These specimens use the same host beam, but the resonance frequencies of the resonators on each beam are different. We further measure the vibration transmittances of these specimens, which give evidence of three interesting band gap phenomena: (i) transition between LR and Bragg band gaps; (ii) near-coupling effect of the local resonance and Bragg scattering; and (iii) resonance frequency of local resonators outside of the LR band gap.

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Low-Frequency Vibration and Radiation Performance of a Locally Resonant Plate Attached with Periodic Multiple Resonators

Applied Sciences ◽

10.3390/app10082843 ◽

2020 ◽

Vol 10 (8) ◽

pp. 2843

Author(s):

Qi Qin ◽

Meiping Sheng ◽

Zhiwei Guo

Keyword(s):

Boundary Conditions ◽

Band Gap ◽

Low Frequency ◽

Expansion Method ◽

Acoustic Power ◽

Radiation Efficiency ◽

Band Gaps ◽

Periodic Arrays ◽

Low Frequency Vibration ◽

The One

The low-frequency vibration and radiation performance of a locally resonant (LR) plate with periodic multiple resonators is studied in this paper, with both infinite and finite structure properties examined. For the finite cases, taking the LR plate attached with two periodic arrays of resonators as an example, the forced vibration response and the radiation efficiency are theoretically derived by adopting a general model with elastic boundary conditions. Through a comparison with the band structures calculated by the plane-wave-expansion method, it shows that the band gaps in the infinite LR plate are in good agreement with the vibration-attenuation bands in the finite LR plate, no matter what boundary conditions are applied to the latter. In contrast to the vibration reduction in the band gaps, the radiation efficiency of the finite LR plate is sharply increased in the band-gap frequency ranges. Furthermore, the acoustic power radiated from the finite LR plate can be seriously affected by its boundary conditions. For the LR plate with greater constraints, the acoustic power is reduced in the band-gap frequency ranges, while that from the one with fully free boundary conditions is increased. When further considering the damping loss factors of the resonators, the attenuation performance can be improved for both the vibration and radiation of the LR plate.

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Investigation on the Band Gap and Negative Properties of Concentric Ring Acoustic Metamaterial

Shock and Vibration ◽

10.1155/2018/1369858 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Meng Chen ◽

Dan Meng ◽

Heng Jiang ◽

Yuren Wang

Keyword(s):

Band Gap ◽

Effective Mass ◽

Coupling Effect ◽

Mass Density ◽

Band Gaps ◽

Acoustic Metamaterials ◽

Concentric Ring ◽

Resonance Modes ◽

Negative Effective Mass ◽

Single Oscillator

The acoustic characteristics of 2D single-oscillator, dual-oscillator, and triple-oscillator acoustic metamaterials were investigated based on concentric ring structures using the finite element method. For the single-oscillator, dual-oscillator, and triple-oscillator models investigated here, the dipolar resonances of the scatterer always induce negative effective mass density, preventing waves from propagating in the structure, thus forming the band gap. As the number of oscillators increases, relative movements between the oscillators generate coupling effect; this increases the number of dipolar resonance modes, causes negative effective mass density in more frequency ranges, and increases the number of band gaps. It can be seen that the number of oscillators in the cell is closely related to the number of band gaps due to the coupling effect, when the filling rate is of a certain value.

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Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance

Journal of Applied Mechanics ◽

10.1115/1.4004592 ◽

2011 ◽

Vol 79 (1) ◽

Cited By ~ 132

Author(s):

Liao Liu ◽

Mahmoud I. Hussein

Keyword(s):

Wave Propagation ◽

Band Structure ◽

Band Gap ◽

Frequency Band ◽

Band Gaps ◽

Flexural Wave ◽

Propagation Mechanism ◽

Bragg Scattering ◽

Frequency Spectra ◽

Local Resonance

Band gaps appear in the frequency spectra of periodic materials and structures. In this work we examine flexural wave propagation in beams and investigate the effects of the various types and properties of periodicity on the frequency band structure, especially the location and width of band gaps. We consider periodicities involving the repeated spatial variation of material, geometry, boundary and/or suspended mass along the span of a beam. In our formulation, we implement Bloch’s theorem for elastic wave propagation and utilize Timoshenko beam theory for the kinematical description of the underlying flexural motion. For the calculation of the frequency band structure we use the transfer matrix method, derived here in generalized form to enable separate or combined consideration of the different types of periodicity. Our results provide band-gap maps as a function of the type and properties of periodicity, and as a prime focus we identify and mathematically characterize the condition for the transition between Bragg scattering and local resonance, each being a unique wave propagation mechanism, and show the effects of this transition on the lowest band gap. The analysis presented can be extended to multi-dimensional phononic crystals and acoustic metamaterials.

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Water waves over arrays of horizontal cylinders: band gaps and Bragg resonance

Journal of Fluid Mechanics ◽

10.1017/s0022112010005471 ◽

2011 ◽

Vol 670 ◽

pp. 504-526 ◽

Cited By ~ 22

Author(s):

C. M. LINTON

Keyword(s):

Band Gap ◽

Water Waves ◽

Band Gaps ◽

Circular Cylinders ◽

Approximate Determination ◽

Systems Of Equations ◽

Periodic Arrays ◽

Horizontal Cylinders ◽

Band Gap Structure

The existence of a band-gap structure associated with water waves propagating over infinite periodic arrays of submerged horizontal circular cylinders in deep water is established. Waves propagating at right angles to the cylinder axes and at an oblique angle are both considered. In each case an exact linear analysis is presented with numerical results obtained by solving truncated systems of equations. Calculations for large finite arrays are also presented, which show the effect of an incident wave having a frequency within a band gap – with the amount of energy transmitted across the array tending to zero as the size of the array is increased. The location of the band gaps is not as predicted by Bragg's law, but we show that an approximate determination of their position can be made very simply if the phase of the transmission coefficient for a single cylinder is known.

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Prediction of local resonance band gaps in 2D elastic metamaterials via Bloch mode identification

Wave Motion ◽

10.1016/j.wavemoti.2021.102734 ◽

2021 ◽

pp. 102734

Author(s):

A. Ragonese ◽

M. Nouh

Keyword(s):

Band Gaps ◽

Local Resonance ◽

Mode Identification ◽

Resonance Band ◽

Bloch Mode ◽

Elastic Metamaterials

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The Band-Gap Studies of Short-Period CdO/MgO Superlattices

Nanoscale Research Letters ◽

10.1186/s11671-021-03517-y ◽

2021 ◽

Vol 16 (1) ◽

Author(s):

Ewa Przeździecka ◽

P. Strąk ◽

A. Wierzbicka ◽

A. Adhikari ◽

A. Lysak ◽

...

Keyword(s):

Band Gap ◽

Layer Thickness ◽

Energy Gap ◽

Band Gaps ◽

Short Period ◽

Wide Range ◽

Salt Structure ◽

Short Period Superlattices ◽

Direct Band ◽

Sublayer Thickness

AbstractTrends in the behavior of band gaps in short-period superlattices (SLs) composed of CdO and MgO layers were analyzed experimentally and theoretically for several thicknesses of CdO sublayers. The optical properties of the SLs were investigated by means of transmittance measurements at room temperature in the wavelength range 200–700 nm. The direct band gap of {CdO/MgO} SLs were tuned from 2.6 to 6 eV by varying the thickness of CdO from 1 to 12 monolayers while maintaining the same MgO layer thickness of 4 monolayers. Obtained values of direct and indirect band gaps are higher than those theoretically calculated by an ab initio method, but follow the same trend. X-ray measurements confirmed the presence of a rock salt structure in the SLs. Two oriented structures (111 and 100) grown on c- and r-oriented sapphire substrates were obtained. The measured lattice parameters increase with CdO layer thickness, and the experimental data are in agreement with the calculated results. This new kind of SL structure may be suitable for use in visible, UV and deep UV optoelectronics, especially because the energy gap can be precisely controlled over a wide range by modulating the sublayer thickness in the superlattices.

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Effect of Double Defects on Transmission Spectra of One-Dimensional Photonic Crystals

Materials Science Forum ◽

10.4028/www.scientific.net/msf.663-665.725 ◽

2010 ◽

Vol 663-665 ◽

pp. 725-728 ◽

Cited By ~ 1

Author(s):

Yuan Ming Huang ◽

Qing Lan Ma ◽

Bao Gai Zhai ◽

Yun Gao Cai

Keyword(s):

Photonic Crystals ◽

Band Gap ◽

Theoretical Calculations ◽

Stop Band ◽

Band Gaps ◽

Characteristic Matrix ◽

Frequency Range ◽

Defect Band ◽

One Dimensional ◽

The One

Considered the model of the one-dimensional photonic crystals (1-D PCs) with double defects, the refractive indexes (n2’, n3’ and n2’’, n3’’) of the double defects were 2.0, 4.0 and 4.0, 2.0 respectively. With parameter n2=1.5, n3=2.5, by theoretical calculations with characteristic matrix method, the results shown that for a certain number (14 was taken) of layers of the 1-D PCs, when the double defects abutted, there was a defect band gap in the stop band gap, while when the double defects separated, there occurred two defect band gaps in the stop band gap; besides, with the separation of the two defects, the transmittance of the double defect band gaps decreased gradually. In addition, in this progress, the frequency range of the stop band gap has a little increase from 0.092 to 0.095.

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The optimum elastic wave band gaps in three dimensional phononic crystals with local resonance

The European Physical Journal B ◽

10.1140/epjb/e2005-00005-y ◽

2004 ◽

Vol 42 (4) ◽

pp. 477-482 ◽

Cited By ~ 9

Author(s):

Xin Zhang ◽

Zhengyou Liu ◽

Youyan Liu

Keyword(s):

Elastic Wave ◽

Three Dimensional ◽

Phononic Crystals ◽

Band Gaps ◽

Wave Band ◽

Local Resonance

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Energy Gaps in BN/GNRs Planar Heterostructure

Materials ◽

10.3390/ma14175079 ◽

2021 ◽

Vol 14 (17) ◽

pp. 5079

Author(s):

Jinyue Guan ◽

Lei Xu

Keyword(s):

Phase Transition ◽

Boron Nitride ◽

Band Gap ◽

Lattice Mismatch ◽

Tight Binding ◽

Graphene Nanoribbon ◽

Band Gaps ◽

Energy Gaps ◽

Local Potentials

Using the tight-binding approach, we study the band gaps of boron nitride (BN)/ graphene nanoribbon (GNR) planar heterostructures, with GNRs embedded in a BN sheet. The width of BN has little effect on the band gap of a heterostructure. The band gap oscillates and decreases from 2.44 eV to 0.26 eV, as the width of armchair GNRs, nA, increases from 1 to 20, while the band gap gradually decreases from 3.13 eV to 0.09 eV, as the width of zigzag GNRs, nZ, increases from 1 to 80. For the planar heterojunctions with either armchair-shaped or zigzag-shaped edges, the band gaps can be manipulated by local potentials, leading to a phase transition from semiconductor to metal. In addition, the influence of lattice mismatch on the band gap is also investigated.

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