Band gap analysis of a three-mass locally resonant structure

Noise & Vibration Worldwide ◽

10.1177/09574565211000411 ◽

2021 ◽

pp. 095745652110004

Author(s):

Preeti Gulia ◽

Arpan Gupta

Keyword(s):

Band Gap ◽

Gap Analysis ◽

Effective Properties ◽

Low Frequency ◽

Band Gaps ◽

Resonant Structure ◽

Resonant System ◽

Mass System ◽

Main Mass ◽

Mass Spring

A mass in a mass locally resonant system has been studied using a numerical and analytical method. This study is performed to compute the band gap and transmission coefficient of a mass–spring locally resonant system. A locally resonant structure is a periodic structure which exhibits negative effective properties in a certain frequency band and reveals band gaps below Bragg’s frequency. In this work, two substructures are attached with main mass so that the system will act as two masses in a mass system. It is found that the presented structure shows two band gaps below 500 Hz with negative effective properties. Addition of a third substructure with the main mass provides an additional band gap at low frequency. The position and width of band gaps can be tuned by changing the values of masses and stiffness.

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Band-Gap Properties of Elastic Metamaterials With Inerter-Based Dynamic Vibration Absorbers

Journal of Applied Mechanics ◽

10.1115/1.4039898 ◽

2018 ◽

Vol 85 (7) ◽

Cited By ~ 9

Author(s):

Xiang Fang ◽

Kuo-Chih Chuang ◽

Xiaoling Jin ◽

Zhilong Huang

Keyword(s):

Band Gap ◽

Frequency Band ◽

Low Frequency ◽

Lattice System ◽

Band Gaps ◽

Vibration Absorbers ◽

Dynamic Vibration ◽

Elastic Metamaterials ◽

Dynamic Vibration Absorbers ◽

Mass Spring

In this paper, inerter-based dynamic vibration absorbers (IDVAs) are applied in elastic metamaterials to broaden low-frequency band gaps. A discrete mass-spring lattice system and a distributed metamaterial beam carrying a periodic array of IDVAs are, respectively, considered. The IDVA consists of a spring and an inerter connected to a traditional mass-spring resonator. Compared to the traditional resonators, the special designed IDVAs generate two local-resonance (LR) band gaps for the discrete lattice system, a narrow low-frequency band gap and a wider high-frequency one. For the distributed IDVA-based metamaterial beam, in addition to the generated two separated LR band gaps, the Bragg band gap can also be significantly broadened and the three band gaps are very close to each other. Being able to amplify inertia, the IDVAs can be relatively light even operated for opening up low-frequency band gaps. When further introducing a dissipative damping mechanism into the IDVA-based metamaterials, the two close-split LR band gaps in the lattice system are merged into one wide band gap. As for the metamaterial beam with the dissipative IDVAs, an even wider band gap can be acquired due to the overlap of the adjacent LR and Bragg-scattering band gaps.

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Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting

Journal of Vibration and Acoustics ◽

10.1115/1.4028378 ◽

2014 ◽

Vol 136 (6) ◽

Cited By ~ 104

Author(s):

Y. Y. Chen ◽

G. L. Huang ◽

C. T. Sun

Keyword(s):

Band Gap ◽

Elastic Waves ◽

Low Frequency ◽

Lattice System ◽

Band Gaps ◽

Negative Capacitance ◽

Bending Waves ◽

Stiffness Constant ◽

Elastic Metamaterials ◽

Gap Control

Elastic metamaterials have been extensively investigated due to their significant effects on controlling propagation of elastic waves. One of the most interesting properties is the generation of band gaps, in which subwavelength elastic waves cannot propagate through. In the study, a new class of active elastic metamaterials with negative capacitance piezoelectric shunting is presented. We first investigated dispersion curves and band gap control of an active mass-in-mass lattice system. The unit cell of the mass-in-mass lattice system consists of the inner masses connected by active linear springs to represent negative capacitance piezoelectric shunting. It was demonstrated that the band gaps can be actively controlled and tuned by varying effective stiffness constant of the linear spring through appropriately selecting the value of negative capacitance. The promising application was then demonstrated in the active elastic metamaterial plate integrated with the negative capacitance shunted piezoelectric patches for band gap control of both the longitudinal and bending waves. It can be found that the location and the extent of the induced band gap of the elastic metamaterial can be effectively tuned by using shunted piezoelectric patch with different values of negative capacitance, especially for extremely low-frequency cases.

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Multi-cavity locally resonant structure with the low frequency and broad band-gaps

AIP Advances ◽

10.1063/1.4968830 ◽

2016 ◽

Vol 6 (11) ◽

pp. 115024 ◽

Cited By ~ 6

Author(s):

Jiulong Jiang ◽

Hong Yao ◽

Jun Du ◽

Jinbo Zhao

Keyword(s):

Broad Band ◽

Low Frequency ◽

Band Gaps ◽

Resonant Structure

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Band Gaps in a Multiresonator Acoustic Metamaterial

Journal of Vibration and Acoustics ◽

10.1115/1.4000784 ◽

2010 ◽

Vol 132 (3) ◽

Cited By ~ 160

Author(s):

G. L. Huang ◽

C. T. Sun

Keyword(s):

Band Gap ◽

Continuum Model ◽

Lattice System ◽

Band Gaps ◽

Equivalent System ◽

Mass System ◽

Acoustic Metamaterial ◽

Single Mass ◽

Band Gap Structure ◽

Gap Structure

In this study, we investigated dispersion curves and the band gap structure of a multiresonator mass-in-mass lattice system. The unit cell of the lattice system consists of three separate masses connected by linear springs. It was demonstrated that the band gaps can be shifted by varying the spring constant and the magnitude of the internal masses. By using the conventional monatomic (single mass) lattice model as an equivalent system, the effective mass was found to become negative for frequencies in the band gaps. An attempt was made to represent the two-resonator mass-in-mass lattice with a microstructure continuum model. It was found that the microstructure continuum model can capture the dispersive behavior and band gap structure of the original two-resonator mass-in-mass system.

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ACOUSTIC BAND GAP FORMATION IN METAMATERIALS

International Journal of Modern Physics B ◽

10.1142/s0217979210057110 ◽

2010 ◽

Vol 24 (25n26) ◽

pp. 4935-4945 ◽

Cited By ~ 2

Author(s):

D. P. ELFORD ◽

L. CHALMERS ◽

F. KUSMARTSEV ◽

G. M. SWALLOWE

Keyword(s):

Band Gap ◽

Lattice Constant ◽

Low Frequency ◽

Band Gaps ◽

Gap Formation ◽

Individual Band ◽

Resonance Band ◽

Frequency Regime ◽

Sonic Crystal ◽

The Individual

We present several new classes of metamaterials and/or locally resonant sonic crystal that are comprised of complex resonators. The proposed systems consist of multiple resonating inclusion that correspond to different excitation frequencies. This causes the formation of multiple overlapped resonance band gaps. We demonstrate theoretically and experimentally that the individual band gaps achieved, span a far greater range (≈ 2kHz) than previously reported cases. The position and width of the band gap is independent of the crystal's lattice constant and forms in the low frequency regime significantly below the conventional Bragg band gap. The broad envelope of individual resonance band gaps is attractive for sound proofing applications and furthermore the devices can be tailored to attenuate lower or higher frequency ranges, i.e., from seismic to ultrasonic.

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Vibration Attenuation Investigations on a Distributed Phononic Crystals Beam for Rubber Concrete Structures

Mathematical Problems in Engineering ◽

10.1155/2021/9982376 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Chao Li ◽

Sifeng Zhang ◽

Liyong Gao ◽

Wei Huang ◽

Zhaoxin Liu

Keyword(s):

Band Gap ◽

Frequency Band ◽

High Frequency ◽

Concrete Beam ◽

Vibration Isolation ◽

Civil Engineering ◽

Low Frequency ◽

Band Gaps ◽

Spring Force ◽

Rubber Concrete

Locally resonant phononic crystals (LRPCs) beam is characterized by the band gaps; some frequency ranges within which flexural waves cannot propagate freely. So, the LRPCs beam can be used for noise or vibration isolation. In this paper, a LRPCs beam with distributed oscillators is proposed, and the general formula of band gaps and transmission spectrum are derived by the transfer matrix method (TMM) and spectrum element method (SEM). Subsequently, the parameter effects on band gaps are investigated in detail. Finally, a rubber concrete beam is designed to demonstrate the application of distributed LRPCs beam in civil engineering. Results reveal that the distributed LRPCs beam has multifrequency band gaps and the number of the band gaps is equal to that of the oscillators. Compared with others, the distributed LRPCs beam can reduce the stress concentration when subjected to vibration. The oscillator interval has no effect on the band gaps, which makes it more convenient to design structures. Individual changes of oscillator mass or stiffness affect the band gap location and width. When the resonance frequency of oscillator is fixed, the starting frequency of the band gap remains constant, and increasing oscillator mass of high-frequency band gap widens the high-frequency band gap, while increasing oscillator mass of low-frequency gap widens both high-frequency and low-frequency band gaps. External loads, such as the common uniform spring force provided by foundation in civil engineering, are conducive to the band gap, and when the spring force increases, all the band gaps are widened. Taken together, a configuration of LRPCs rubber concrete beam is designed, and it shows good isolation on the vibration induced by the railway. By the presented design flow chart, the research can serve as a reference for vibration isolation of LRPCs beams in civil engineering.

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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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Multi-cavity coupling acoustic metamaterials with low-frequency broad band gaps based on negative mass density

Modern Physics Letters B ◽

10.1142/s0217984916503176 ◽

2016 ◽

Vol 30 (23) ◽

pp. 1650317

Author(s):

Chuanhui Yang ◽

Jiu Hui Wu ◽

Songhua Cao ◽

Li Jing

Keyword(s):

Band Gap ◽

Mass Density ◽

Resonant Cavity ◽

Broad Band ◽

Low Frequency ◽

Band Gaps ◽

Acoustic Metamaterials ◽

Negative Mass ◽

Closed Cavity ◽

Cavity Coupling

This paper studies a novel kind of low-frequency broadband acoustic metamaterials with small size based on the mechanisms of negative mass density and multi-cavity coupling. The structure consists of a closed resonant cavity and an open resonant cavity, which can be equivalent to a homogeneous medium with effective negative mass density in a certain frequency range by using the parameter inversion method. The negative mass density makes the anti-resonance area increased, which results in broadened band gaps greatly. Owing to the multi-cavity coupling mechanism, the local resonances of the lower frequency mainly occur in the closed cavity, while the local resonances of the higher frequency mainly in the open cavity. Upon the interaction between the negative mass density and the multi-cavity coupling, there exists two broad band gaps in the range of 0–1800 Hz, i.e. the first-order band gap from 195 Hz to 660 Hz with the bandwidth of 465 Hz and the second-order band gap from 1157 Hz to 1663 Hz with the bandwidth of 506 Hz. The acoustic metamaterials with small size presented in this paper could provide a new approach to reduce the low-frequency broadband noises.

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PERFECT OPTICAL TRANSPORT AND OPTICAL BAND GAP IN QUASIPERIODIC SUPERLATTICES

Modern Physics Letters B ◽

10.1142/s0217984912501102 ◽

2012 ◽

Vol 26 (17) ◽

pp. 1250110

Author(s):

XIA YU ◽

KE-QIU CHEN ◽

YAN ZHANG

Keyword(s):

Refractive Index ◽

Band Gap ◽

Optical Band Gap ◽

Negative Refractive Index ◽

Low Frequency ◽

Wide Band ◽

Band Gaps ◽

Transmission Coefficients ◽

Refractive Index Material ◽

Superlattice Structures

A three-component quasiperiodic superlattice structures composing of both positive and negative refractive index materials are shown to display resonant transport behavior and optical band gaps. When the structure is composed of nondispersive refractive index material, the number of the resonant transmission peaks increases and the optical band gap becomes broad with the increasing of the medium generation. The band gap covers all the wavelength except for some singular wavelength points when the structure is composed of negative refractive index materials. Moreover, it is found that the spectrum shifts to low frequency for oblique incidence. And with the increasing of the optical thickness, the band gap splits and new perfect transport channels emerge. For a more realistic dispersive negative refractive index material, the transmission coefficients are characterized by a rich transmission profile without symmetry, more wide band gaps and abundance transmissive channels appear.

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