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.

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.

Temperature effects on the band gaps of Lamb waves in a one-dimensional phononic-crystal plate (L)

2011 ◽  
Vol 129 (3) ◽  
pp. 1157-1160 ◽  
Author(s):  
Y. Cheng ◽  
X. J. Liu ◽  
D. J. Wu
Keyword(s):  
Temperature Effects ◽  
Lamb Waves ◽  
Phononic Crystal ◽  
Crystal Plate ◽  
Band Gaps ◽  
One Dimensional

Propagation of Lamb Waves in Phononic-Crystal Plates

2007 ◽  
Vol 23 (3) ◽  
pp. 223-228 ◽  
Author(s):  
J.-C. Hsu ◽  
T.-T. Wu
Keyword(s):  
Band Gap ◽  
Triangular Lattice ◽  
Lamb Waves ◽  
Phononic Crystal ◽  
Plate Thickness ◽  
Expansion Method ◽  
Band Gaps ◽  
Square Lattice ◽  
Pass Band ◽  
Band Structures

AbstractIn this paper, the band structures of Lamb waves in the two-dimensional phononic-crystal plates are calculated and analyzed based on the plane wave expansion method. The phononic-crystal plates are composed of an array of circular crystalline iron cylinders embedded in the epoxy matrix. Square lattice and triangular lattice are analyzed and discussed, respectively. For the square lattice, two complete band gaps exist, and a narrow pass band between the complete band gaps separates them apart. For the triangular lattice, a wide complete band gap existing with the ratio of gap width to midgap frequency Δω/ωm equal to 72% is found. Furthermore, the influence of the plate thickness is crucial for band structures of Lamb waves. Tuning plate thickness can shift the pass bands effectively, and band shifting causes the variation of the width of complete band gap and its opening and closure.

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.

Thermal Tuning of Band Structures in a One-Dimensional Phononic Crystal

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Zuguang Bian ◽  
Wei Peng ◽  
Jizhou Song
Keyword(s):  
Band Gap ◽  
Acoustic Waves ◽  
Vibration Isolation ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Polybutylene Terephthalate ◽  
Band Structures ◽  
One Dimensional ◽  
Thermal Tuning

Phononic crystals make the realization of complete acoustic band gaps possible, which suggests many applications such as vibration isolation, noise suppression, acoustic barriers, filters, wave guides, and transducers. In this paper, an analytic model, based on the transfer matrix method, is developed to study the band structures of bulk acoustic waves including SH-, P-, and SV-waves in a one-dimensional phononic crystal, which is formed by alternating strips of two different materials. The analysis is demonstrated by the phononic crystal of Ba0.7Sr0.3TiO3 (BST) and polybutylene terephthalate (PBT), whose elastic properties depend strongly on the temperature. The results show that some band gaps are very sensitive to the temperature. Depending on the wave mode, the center frequency of the first band gap may decrease over 25% and band gap width may decrease over 60% as the temperature increases from 30 °C to 50 °C. The transmission of acoustic waves in a finite phononic crystal is also studied through the coefficient of transmission power. These results are very useful for the design and optimization of thermal tuning of phononic crystals.

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 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.

Vibration Isolation Design for Periodical Stiffened Shells by the Wave Finite Element Method

2017 ◽  
Author(s):  
Jie Hong ◽  
Xueqing He ◽  
Dayi Zhang ◽  
Yanhong Ma
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Band Gap ◽  
Vibration Isolation ◽  
Band Gaps ◽  
Vibration Band ◽  
Frequency Range ◽  
Gap Characteristics ◽  
Plates And Shells ◽  
Element Method

Thin plates and shells are widely used to reduce the weight in modern mechanical systems, in particularly for the aeronautic and astronautical machineries. These thin structures can result in intensive modes, and lead to the difficulty on the suppression of vibration. The excessive vibration of casing can not only lead to the failure itself but also has a significant influence on the related external pipelines and other attachments which could cause the fatigue failure for the aero-engine casings. A proper method is needed to investigate the dynamic characteristics for these casings, and to be potentially further used for the vibration isolation design. Periodic structure has received a great deal of attentions for its band gap characteristics. Sound and other vibration can be forbidden to propagate in its band gap. With regard to the applications in aero-engines, the article provides one probable vibration isolation method for the stiffened plates and shells with high strength-to-weight ratio and with periodic configuration characteristics. The vibration characteristics of the stiffened shell are usually difficult to be acquired, and there is neither an analytical solution for the complicated stiffeners configuration. Therefore, a Wave finite element method (FEM) based on the wave theory and finite element method, which can solve the dynamic response and band gap characteristics of casings with wide frequency band is presented. Taking the characteristics of the curvature into account, it is proposed for how to confirm the periodic boundaries of the shells. Moreover, the finite element model built by ANSYS is combined with MATLAB program, and the validity of Wave FEM is proved in shell with different boundaries including free-clamped boundary and free-free boundary. The results reveal that with the increase of stiffeners’ width, wider frequency range and larger attenuating ability appear in the vibration band gap. While with the increase of stiffeners’ thickness, neither the variety of the attenuating capability nor of the frequency range of band gaps is monotone. And the local resonance of stiffeners is obvious, the corresponding band gaps’ contribution to the whole system is little. Moreover, three typical configurations-hexagonal, square and triangular are considered. The configurations of stiffeners have distinct characteristics on the dispersion relation, if the weight problems are not taken into account, the square honeycomb is better than the others.

Research On Band Gap Characteristics Of Pmma/Ai Criss-Crossed Elliptical Holes Phononic Crystal Plate

2021 ◽  
Author(s):  
Zhuo-te Wu ◽  
Ben-jie Ding ◽  
Xue-yong Zhou ◽  
Kun-peng Chen ◽  
Minghua Zhang ◽  
...  
Keyword(s):  
Band Gap ◽  
Phononic Crystal ◽  
Crystal Plate ◽  
Gap Characteristics ◽  
Elliptical Holes

Band gap and defect state engineering in a multi-stub phononic crystal plate

2015 ◽  
Vol 117 (15) ◽  
pp. 154301 ◽  
Author(s):  
Ping Jiang ◽  
Xiao-Peng Wang ◽  
Tian-Ning Chen ◽  
Jian Zhu
Keyword(s):  
Band Gap ◽  
Phononic Crystal ◽  
Crystal Plate ◽  
Defect State
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