Transmission properties of locally resonant sonic materials with finite slab thickness

2005 ◽  
Vol 220 (9-10) ◽  
Author(s):  
Kin Hung Fung ◽  
Zhengyou Liu ◽  
Che Ting Chan
Keyword(s):  
Composite Material ◽  
Simple Model ◽  
Band Gap ◽  
Scattering Theory ◽  
Band Gaps ◽  
Slab Thickness ◽  
Frequency Range ◽  
Filling Fraction ◽  
Transmission Properties ◽  
Finite Slab

AbstractUsing multiple-scattering theory, we studied the transmission properties of a slab of composite material that have sonic band gaps due to local resonances. Thin slabs of such material have transmission properties that are apparently different from conventional band gap material. For example, there can be transmission peaks in the frequency range inside the bulk sonic band gap. If the slab thickness is changed, we found that the top of band gap shifts while the bottom of band gap, being pinned by the resonance frequency, does not. By changing the slab thickness, the “effective band gap” may be narrowed or broadened, depending on the filling fraction of the locally resonant units. In order to provide an intuitive understanding of the phenomena, we constructed a simple model to understand the phenomena by comparing its transmission and band structure with that of the locally resonant sonic materials.

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.

Wave propagation in acoustic metamaterials with resonantly shunted cross-shape piezos

2018 ◽  
Vol 29 (13) ◽  
pp. 2744-2753 ◽  
Author(s):  
Shengbing Chen
Keyword(s):  
Wave Propagation ◽  
Band Gap ◽  
Vibration Isolation ◽  
Band Gaps ◽  
Acoustic Metamaterials ◽  
Resonant Frequencies ◽  
Piezoelectric Patch ◽  
Transmission Properties ◽  
Gap Width ◽  
Band Gap Width

Cross-shape piezoelectric patches were originally proposed to improve the band-gap properties of acoustic metamaterials with shunting circuits. The dispersion curves are characterized through the application of finite element method. Also, the theoretical band-gap predictions are verified by simulation results obtained from COMSOL. The investigation results show that the proposed scheme distinguishes itself from the conventional square patches by broader band gaps, whose bandwidth is almost doubled. The inherent capacitance of the piezoelectric patch is strongly related to the boundary conditions, so the local resonant band gap is strongly affected by the shape of piezoelectric patches as well. As a result, the band-gap width and location of metamaterials with different shape patches are rather different, even with the same size patches. Also, negative modulus (NM) and Poisson’s ratio were observed around the resonant frequencies. The transmission properties of finite periods agree well with band-gap predictions. An obvious attenuation zone (AZ) is produced around the band-gap location, in which the wave propagation is decayed strongly. Similarly, the width of AZ of the proposed metamaterial is much larger than that of the conventional one. Hence, the proposed scheme demonstrates more advantages in the application to vibration isolation when compared with the conventional.

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.

Lamb wave band gaps in one-dimensional radial phononic crystal slabs

2015 ◽  
Vol 29 (03) ◽  
pp. 1550002 ◽  
Author(s):  
Yinggang Li ◽  
Tianning Chen ◽  
Xiaopeng Wang
Keyword(s):  
Finite Element ◽  
Axial Symmetry ◽  
Lamb Wave ◽  
Lamb Waves ◽  
Phononic Crystal ◽  
Band Gaps ◽  
Slab Thickness ◽  
Wave Band ◽  
Filling Fraction ◽  
One Dimensional

In this paper, we theoretically investigate the band structures of Lamb wave in one-dimensional radial phononic crystal (PC) slabs composed of a series of alternating strips of epoxy and aluminum. The dispersion relations, the power transmission spectra and the displacement fields of the eigenmodes are calculated by using the finite element method based on two-dimensional axial symmetry models in cylindrical coordinates. The axial symmetry model is validated by three-dimensional finite element model in Cartesian coordinates. Numerical results show that the proposed radial PC slabs can yield several complete band gaps with a variable bandwidth exist for elastic waves. Furthermore, the effects of the filling fraction and the slab thickness on the band gaps are further explored numerically. It is worth observing that, with the increase of the filling fraction, both the lower and upper edges of the band gaps are simultaneously shifted to higher frequency, which results from the enhancement interaction between the rigid resonance of the scatterer and the matrix. The slab thickness is the key parameter for the existence and the width of complete band gaps in the radial PC slabs. These properties of Lamb waves in the radial PC plates can potentially be applied to optimize band gaps, generate filters and design acoustic devices in the rotary machines and structures.

Influence of Point Defects on Band Gaps of Fe-Epoxy in Two-Dimensional Phononic Crystal

2013 ◽  
Vol 652-654 ◽  
pp. 1377-1382
Author(s):  
Jiao He ◽  
Guang Hui Fan ◽  
De Xun Zhao ◽  
Ying Kai Liu
Keyword(s):  
Point Defect ◽  
Band Gap ◽  
Nearest Neighbor ◽  
Phononic Crystal ◽  
Expansion Method ◽  
Band Gaps ◽  
Two Dimensional ◽  
Defect States ◽  
Filling Fraction ◽  
Nearest Neighbor Coupling

The band gap of a new two-dimensional phononic crystal was studied by the plane-wave expansion method. The two-dimensional phononic crystal is formed by square-shape array geometry of iron cylinders with square cross section inserted in an epoxy resin. The band gaps of different structures were calculated such as defect-free, single cavity crystal point defect states, crystal point defect states with (10) direction coupling, crystal point defect states with (10) direction next-nearest-neighbor coupling, and crystal point defect states with (11) direction next-nearest-neighbor coupling. Compared with that of defect-free, it is conclude that point defect is beneficial to the production of band gaps. The bandwidth of point defect is about 5 times larger than that of the defect-free crystal with the filling fraction F=0.4. In addition, the maximum number of band gap is in the crystal point defect states with (10) direction next-nearest-neighbor coupling. It will provide a theoretical reference for the manufacture of phononic crystal.

Study on Band Gap Varying of Diamond Photonic Crystals by Fabricating to Bring the Error of Dielectric Volume Fraction

2014 ◽  
Vol 670-671 ◽  
pp. 101-104
Author(s):  
Shi Bin Chen ◽  
Yun Shi Yao ◽  
Xiao Hui Li ◽  
Min Jie Wang
Keyword(s):  
Photonic Crystals ◽  
Band Gap ◽  
Volume Fraction ◽  
Band Gaps ◽  
Band Width ◽  
Photonic Band Gaps ◽  
Frequency Range ◽  
Gel Casting ◽  
Diamond Crystals ◽  
Photonic Band

To avoid the effect of the error of dielectric volume fraction brought by fabricating process on band gap, the diamond crystals with different the error of dielectric volume fraction were designed and fabricated to investigate the fluctuation of band gaps. Theses photonic crystals with a diamond structure were fabricated using alumina by stereolithography, gel-casting and sintering. The photonic band gaps were observed along <100> direction and the photonic band gaps were formed in different frequency range. Increasing the radius from 4.2mm to 4.32mm and changing band width from 0.8 to 1.39GHz, the radius is increased by 2.86%, and corresponding band width increased by 73.75%. Therefore, the fabrication error in mold and fabrication process including injecting mold, sintering should be maintained under the same conditions, which can retain the error of band gap.

scholarly journals Study on Lamb Waves in a Composite Phononic Crystal Plate

Crystals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 799
Author(s):  
Lili Yuan ◽  
Peng Zhao ◽  
Yong Ding ◽  
Benjie Ding ◽  
Jianke Du ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Band Gap ◽  
Vibration Isolation ◽  
Lamb Waves ◽  
Phononic Crystal ◽  
Volume Ratio ◽  
Geometric Parameters ◽  
Crystal Plate ◽  
Band Gaps ◽  
Frequency Range

In the paper, a phononic crystal plate composed of a magnetorheological elastomer with adjustable band gaps in the low frequency range is constructed. The dispersion relations of Lamb waves are studied by the supercell plane wave expansion method. The transmission responses as well as the displacement fields of Lamb waves are calculated by the finite element method. The influence of geometric parameters on the band gaps, the regulation effect of the volume ratio of Fe particles and the bias magnetic field on the band gaps are analyzed. Based on the numerical results, we find that the volume ratio of Fe particles and the magnetic field affect the band gap effectively. The location and width of the band gaps can be adjusted within a broad frequency range by varying the geometric parameters and magnetic field. We can control the band gap, achieve an appropriate and wide low band gap by selecting proper geometric parameters and applying an external contactless magnetic field to deal with complicated and changeable engineering environment. The results are useful for understanding and optimizing the design of composite vibration isolation plates.

Vibration isolation characteristics of finite periodic tetra-chiral lattice coating filled with internal resonators

2016 ◽  
Vol 230 (16) ◽  
pp. 2840-2850 ◽  
Author(s):  
Dawei Zhu ◽  
Xiuchang Huang ◽  
Hongxing Hua ◽  
Hui Zheng
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Band Gaps ◽  
Stiffened Plate ◽  
Frequency Range ◽  
Vibration Attenuation ◽  
Unit Cells ◽  
Internal Resonators

Owing to their locally resonant mechanism, internal resonators are usually used to provide band gaps in low-frequency region for many types of periodic structures. In this study, internal resonators are used to improve the vibration attenuation ability of finite periodic tetra-chiral coating, enabling high reduction of the radiated sound power by a vibrating stiffened plate. Based on the Bloch theorem and finite element method, the band gap characteristics of tetra-chiral unit cells filled with and without internal resonators are analysed and compared to reveal the relationship between band gaps and vibration modes of such tetra-chiral unit cells. The rotational vibration of internal resonators can effectively strengthen the vibration attenuation ability of tetra-chiral lattice and extend the effective frequency range of vibration attenuation. Two tetra-chiral lattices with and without internal resonators are respectively designed and their vibration transmissibilities are measured using the hammering method. The experimental results confirm the vibration isolation effect of the internal resonators on the finite periodic tetra-chiral lattice. The tetra-chiral lattice as an acoustic coating is applied to a stiffened plate, and analysis results indicate that the internal resonators can obviously enhance the vibration attenuation ability of tetra-chiral lattice coating in the frequency range of the band gap corresponding to the rotating vibration mode of internal resonators. When the soft rubber with the internal resonators in tetra-chiral layers has gradient elastic modulus, the vibration attenuation ability and noise reduction of the tetra-chiral lattice coating are basically enhanced in the frequency range of the corresponding band gaps of tetra-chiral unit cells.

scholarly journals Surface acoustic wave band gaps in micro-machined air/silicon phononic structures — theoretical calculation and experiment

2005 ◽  
Vol 220 (9-10) ◽  
Author(s):  
Tsung-Tsong Wu ◽  
Zi-Gui Huang ◽  
Shih-Yang Liu
Keyword(s):  
Acoustic Wave ◽  
Band Gap ◽  
Surface Acoustic Wave ◽  
High Frequency ◽  
Expansion Method ◽  
Band Gaps ◽  
Wave Band ◽  
Filling Fraction ◽  
Saw Devices ◽  
Experimental Side

AbstractIn this paper, we investigate the band gaps of micro-machined air/silicon phononic structures both theoretically and experimentally. Based on the plane wave expansion method, dispersion relations of the surface and bulk modes with square lattices in air/silicon two-dimensional phononic structures are calculated and discussed. Band gap widths due to the filling fraction and temperature variation are also analyzed. On the experimental side, generation and reception of high frequency surface acoustic wave in this band structure are realized by a pair of interdigital transducers (IDT) with frequency around 200 MHz. Details of the fabricating process of the phononic structure and the high frequency surface wave generating and receiving IDTs are given. The results demonstrate clearly the existence of SAW band gap in the micro-machined phononic structure and this study may serve as a basis for studying the band gap of SAW in micro-machined phononic structure with the dimension in the order of micrometer and find applications in the RF SAW devices.

scholarly journals Research on the Band Gap Characteristics of Two-Dimensional Phononic Crystals Microcavity with Local Resonant Structure

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mao Liu ◽  
Pei Li ◽  
Yongteng Zhong ◽  
Jiawei Xiang
Keyword(s):  
Band Gap ◽  
Phononic Crystal ◽  
Engineering Application ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Wave Band ◽  
Two Dimensional ◽  
Frequency Range ◽  
Gap Characteristics

A new two-dimensional locally resonant phononic crystal with microcavity structure is proposed. The acoustic wave band gap characteristics of this new structure are studied using finite element method. At the same time, the corresponding displacement eigenmodes of the band edges of the lowest band gap and the transmission spectrum are calculated. The results proved that phononic crystals with microcavity structure exhibited complete band gaps in low-frequency range. The eigenfrequency of the lower edge of the first gap is lower than no microcavity structure. However, for no microcavity structure type of quadrilateral phononic crystal plate, the second band gap disappeared and the frequency range of the first band gap is relatively narrow. The main reason for appearing low-frequency band gaps is that the proposed phononic crystal introduced the local resonant microcavity structure. This study provides a good support for engineering application such as low-frequency vibration attenuation and noise control.

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