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

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.

Evidence for complete low-frequency vibration band gaps in a thick elastic steel metamaterial plate

2019 ◽  
Vol 33 (04) ◽  
pp. 1950038 ◽  
Author(s):  
Suobin Li ◽  
Yihua Dou ◽  
Tianning Chen ◽  
Zhiguo Wan ◽  
Jingjing Huang ◽  
...  
Keyword(s):  
Band Gap ◽  
Steel Plate ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Crystal Plate ◽  
Band Gaps ◽  
Formation Mechanisms ◽  
Vibration Band ◽  
Low Frequency Vibration ◽  
Thick Steel

Elastic steel metamaterial plates can be used for noise- and vibration-reduction due to unique physical properties related to their vibration band gap. However, obtaining a complete low-frequency vibration band gap in a thick elastic steel metamaterial plate is difficult. In this paper, we simulate a complete low-frequency vibration band gap in a thick elastic steel metamaterial plate. The structure consists of periodic, double-sided, composite stepped resonators, which were deposited on a 2D locally resonant phononic crystal plate. The phononic crystal plate consists of an array of rubber fillers embedded in a thick steel plate. The dispersion relations, power-transmission spectra, and the displacement fields of the eigenmodes are calculated using the finite-element method. The results show that, for the proposed structure, the opening of the first complete vibration band gap is reduced by a factor of 9.5 compared to a conventional thick elastic steel metamaterial plate. This causes attenuation of low-frequency elastic waves. The formation mechanisms for the vibration band gap are also explored numerically. The results indicate that the formation mechanism for the new low-frequency vibration band gap can be attributed to coupling between a local resonance mode of the composite stepped resonators and the Lamb wave mode of the thick steel-plate. The location of the vibration band gap is determined by the resonator mode of the composite stepped resonators. The vibration band gap effects of the composite stepped resonators are also investigated in this paper. We find that the location of the complete vibration band gaps can be modulated with a relatively low frequency using different composite stepped resonators. Such an elastic steel metamaterial plate with a complete low-frequency vibration band gap can be used to reduce both vibration and noise in various commercial and research applications.

An Inertant Elastic Metamaterial Plate With Extra Wide Low-Frequency Flexural Band Gaps

2020 ◽  
Vol 88 (2) ◽  
Author(s):  
Xiang Fang ◽  
Kuo-Chih Chuang ◽  
Xiao-Ling Jin ◽  
Dan-Feng Wang ◽  
Zhi-Long Huang
Keyword(s):  
Vibration Suppression ◽  
Low Frequency ◽  
Wide Band ◽  
Band Gaps ◽  
Flexural Wave ◽  
Additional Degree ◽  
Periodic Arrays ◽  
Low Frequency Vibration ◽  
Elastic Metamaterial Plate ◽  
Engineering Vibration

Abstract Arranging inerter arrays in designing metamaterials can achieve low-frequency vibration suppression even with a small configuration mass. In this work, we investigate flexural wave bandgap properties of an elastic metamaterial plate with periodic arrays of inerter-based dynamic vibration absorbers (IDVAs). By extending the plane wave expansion (PWE) method, the inertant elastic metamaterial plate is explicitly formulated in which the interactions of the attached IDVAs and the host plate are considered. Due to the additional degree-of-freedom induced by each IDVA, multiple band gaps are obtained. Along the ΓX direction, the inertant elastic metamaterial plate exhibits two locally resonant (LR) band gaps and one Bragg (BG) band gap. In contrast, along the ΓM direction, two adjacent LR band gaps are obtained. Detailed parametric analyses are conducted to investigate the relationships between the flexural wave bandgap properties and the structural inertant parameters. With a dissipative mechanism added to the IDVAs, extremely wide band gaps in different directions can be further generated. Finally, by adopting an effective added mass technique in the finite element method, displacement transmission and vibration modes of a finite inertant elastic metamaterial plate are obtained. Our investigation indicates that the proposed inertant elastic metamaterial plate has extra-wide low-frequency flexural band gaps and therefore has potential applications in engineering vibration prohibition.

The effects of composite primitive cells on band gap property of locally resonant phononic crystal

2021 ◽  
pp. 2150334
Author(s):  
Lijian Lei ◽  
Linchang Miao ◽  
Chao Li ◽  
Xiaodong Liang ◽  
Junjie Wang
Keyword(s):  
Band Gap ◽  
Formation Mechanism ◽  
Phononic Crystal ◽  
Engineering Application ◽  
Low Frequency ◽  
Structure Design ◽  
Band Gaps ◽  
Gap Formation ◽  
Cell Spacing ◽  
Low Frequency Vibration

Locally resonant phononic crystal (LRPC) has the extraordinary property to prohibit the wave propagation in specific low-frequency ranges, however it exists limitation in engineering application due to narrow band gap width. Extensive achievements have been obtained on the locally resonant band gap (LRBG) tunability, whereas existing investigations mainly concern the independent primitive cells structure, which have the limitation in obtaining low-frequency and broadband simultaneously. In this paper, the composited locally resonant phononic crystals (CLRPC) are proposed and the effects of primitive cells contact state on the LRBG properties are investigated. The dispersion curves are applied to obtain the LRBG, and the corresponding modal features are analyzed to explain the band gap formation mechanism. The band structure indicates the design of composite primitive cells is able to increase the band gap number and obtain lower band gap, which is verified by the frequency response function (FRF). For the band gap formation mechanism, the asymmetric vibration due to primitive cells contact leads to diverse and strong coupling response, which generates more band gaps and reduces the band gap starting frequency, therefore the band gaps can be tuned by designing carefully the geometry structure of CLRPC. Further researches on band gap optimization demonstrate that the smaller cell spacing, smaller lattice constant and larger damping of coating layer should be satisfied to obtain broader LRBG and considerable attenuation synchronously. This investigation can provide references for the locally resonant isolation structure design in the low-frequency vibration control field.

A novel metal-matrix phononic crystal with a low-frequency, broad and complete, locally-resonant band gap

2018 ◽  
Vol 32 (19) ◽  
pp. 1850221 ◽  
Author(s):  
Suobin Li ◽  
Yihua Dou ◽  
Tianning Chen ◽  
Zhiguo Wan ◽  
Zhengrong Guan
Keyword(s):  
Band Gap ◽  
Metal Matrix ◽  
Steel Plate ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Crystal Plate ◽  
Band Gaps ◽  
Frequency Range ◽  
Low Frequency Vibration ◽  
Out Of Plane

In this paper, a novel metal-matrix phononic crystal with a low-frequency, broad and complete, locally-resonant band gap, which includes the in-plane and out-of-plane band gaps, is investigated numerically. The proposed structure consists of double-sided single “hard” cylinder stubs, which are deposited on a two-dimensional locally-resonant phononic-crystal plate that consists of an array of rubber fillers embedded in a steel plate. Our results indicate that both the out-of-plane band gap and the in-plane band gap increase after introducing single “hard” cylinder stubs. More specifically, the out-of-plane band gap is increased by the out-of-plane analogous-rigid mode, while the in-plane band gap is increased by the in-plane analogous-rigid mode. The out-of-plane and the in-plane analogous-rigid mode are formed after introduction of the single “hard” cylinder stub. As a result, a broad, complete locally-resonant band gap in the low frequency is obtained due to the broad in-plane and out-of-plane band gaps overlapping. Compared to the classical double-sided stubbed metal-matrix phononic-crystal plate, the absolute bandwidth of the complete band gap is increased by a factor of 4.76 in the proposed structure. Furthermore, the effect of simple “hard” stubs on complete band gaps is investigated. The results show that the location of the complete band gaps can be modulated using a low frequency, and the bandwidth can be extended to a larger frequency range using different “hard” stubs. The new structure provides an effective way for metal-matrix phononic crystals to obtain broad and complete locally-resonant band gaps in the low-frequency range, which has many applications for low-frequency vibration reduction.

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

2010 ◽  
Vol 663-665 ◽  
pp. 725-728 ◽  
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.

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

2014 ◽  
Vol 136 (6) ◽  
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.

Acoustic Barriers Based on Sonic Crystals

2007 ◽  
Author(s):  
V. Romero-Garci´a ◽  
E. Fuster-Garcia ◽  
L. M. Garci´a-Raffi ◽  
J. V. Sa´nchez-Pe´rez
Keyword(s):  
Geometric Distribution ◽  
Free Field ◽  
Low Frequency ◽  
Optimization Methods ◽  
Band Gaps ◽  
High Symmetry ◽  
Low Frequencies ◽  
Periodic Arrays ◽  
Sonic Crystals ◽  
High Sound

Environmental noise problems become an standard topic across the years. Acoustic barriers have been purposed as a possible solution because they can act creating an acoustic attenuation zone which depends on the sound frequency, reducing the sound transmission through it. It was demonstrated that at high sound frequencies the effect of the barriers is more pronounced than at low frequencies, due to the diffraction in their edges. Sonic Crystals (SCs) are periodic arrays of scatterers embedded in a host material with strong modulation of its physical properties, that produces band gaps attenuation in frequencies related with their geometry. These frequencies are explained by the well known Bragg’s diffraction inside the crystal. SCs present different high symmetry directions, where the Bragg’s peaks appears in different frequencies ranges due to the variation of the geometry in each direction. Recently, some authors have studied the possibility to use SCs to reduce noise in free-field condition. Also, it was showed that SCs built by trees are acoustic systems that present acoustic band gaps in low frequency range due to the geometric distribution of the trees. These results led us think that these structures are a suitable device to reduce noise, this means SCs could be use as acoustic barriers. Nevertheless the technological application of these devices for controlling the noise present some problems. First, the angular dependence of the frequencies attenuated when the sound impinges over the SC. Second, the fact that the necessary space to put the SC is bigger than in the case of the traditional acoustic barriers. Finally, the necessity of some robust and long-lasting materials to use them outdoors. In this paper we show the possibility to use different materials (rigid, mixed or soft) to make scatterers, explaining their advantages or disadvantages. These materials in conjunction with some optimization methods will allow us find some solutions to the problems mentioned above. We will relate both acoustic systems, acoustic barriers and SCs, making a comparison of the main properties of each one and then, we will present the technological possibilities to design acoustic barriers based on SCs.

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

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Yong Xiao ◽  
Jihong Wen ◽  
Gang Wang ◽  
Xisen Wen
Keyword(s):  
Band Gap ◽  
Coupling Effect ◽  
Numerical Study ◽  
Spectral Element ◽  
Band Gaps ◽  
Local Resonance ◽  
Periodic Arrays ◽  
Finite Structures ◽  
Resonance Frequencies ◽  
Vibration Transmittance

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.

Flexural Vibration Band Gaps in a Ternary Phononic Crystal Thin Plate

2011 ◽  
Vol 675-677 ◽  
pp. 1085-1088
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Jian Bao Li
Keyword(s):  
Band Gap ◽  
Thin Plate ◽  
Mass Density ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Expansion Method ◽  
Band Gaps ◽  
Physical Parameters ◽  
Vibration Band ◽  
Filling Fraction

The band structures of flexural waves in a ternary locally resonant phononic crystal thin plate are studied using the improved plane wave expansion method. And the thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps of flexural vibration with low frequency are shown. The calculation results show that the band gap width is strongly dependent on the filling fraction, the radius ratio, the mass density and the Young’s modulus contrasts between the core and the coating. So by changing these physical parameters, the required band gap could be obtained.

scholarly journals ACOUSTIC BAND GAP FORMATION IN METAMATERIALS

2010 ◽  
Vol 24 (25n26) ◽  
pp. 4935-4945 ◽  
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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