scholarly journals Study on Tunable Band Gap of Flexural Vibration in a Phononic Crystals Beam with PBT

Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1346
Author(s):  
Peng Zhao ◽  
Lili Yuan ◽  
Tingfeng Ma ◽  
Hanxing Wei
Keyword(s):  
Band Gap ◽  
Elastic Foundation ◽  
Vibration Isolation ◽  
Axial Stress ◽  
Low Frequency ◽  
Flexural Vibration ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Response Curves ◽  
Element Method

Low-frequency flexural vibration plays a significant role in beam vibration control. To efficiently attenuate the propagation of flexural vibration at a low-frequency range, this paper proposes a new type of a phononic crystals beam with an adjustable band gap. The governing equations of flexural vibration in a periodic beam are established based on the Euler theory and Timoshenko theory. The band structures are calculated by the plane wave expansion method, the attenuation properties and transmission response curves with a finite periodic beam are calculated by the spectral element method and finite element method. The effects of the elastic foundation and axial stress on band gaps are discussed in detail, and the regulation of the temperature field on the band gap is emphatically studied. The theoretical and numerical results show that the elastic foundation and axial stress have significant influence on the band gap, and the location and width of the band gaps can be adjusted effectively when the Young’s modulus of PBT is changed by a varying temperature. The results are very useful for understanding and optimizing the design for composite vibration isolation beams.

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

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.

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.

scholarly journals Band Gaps and Vibration Isolation of a Three-dimensional Metamaterial with a Star Structure

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3812 ◽  
Author(s):  
Heng Jiang ◽  
Mangong Zhang ◽  
Yu Liu ◽  
Dongliang Pei ◽  
Meng Chen ◽  
...  
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Mass Density ◽  
Three Dimensional ◽  
Low Frequency ◽  
Band Gaps ◽  
Acoustic Metamaterials ◽  
Star Structure

Elastic metamaterials have promising applications in wave control and vibration isolation, due to their extraordinary characteristics, e.g., negative Poisson ratio, band gaps, effective negative mass density and effective negative modulus. How to develop new functional metamaterials using a special structure has always been a hot topic in this field. In this study, a three-dimensional (3D) star structure is designed to construct metamaterials with both negative static and dynamic properties. The results show that the 3D star structure formed a wide band gap at lower frequency and had a negative Poisson’s ratio. Different from conventional acoustic metamaterials, the main physical mechanism behind the low-frequency band gap of the 3D star structure is the resonance mode formed by the bending deformation of each rib plate, which made it easier to achieve effective isolation of low-frequency elastic waves with a low mass density. In addition, many structural parameters of the 3D star structure can be modulated to effectively adjust the band gap frequency by changing the angle between the concave nodes and aspect ratio. This study provides a new way to design the 3D acoustic metamaterials and develop the lightweight vibration isolation devices.

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.

Flexural vibration band gaps of the multiple local resonance elastic metamaterial plates with irregular resonators

2019 ◽  
Vol 33 (33) ◽  
pp. 1950409
Author(s):  
Guo Li ◽  
Yake Dong ◽  
Genquan Li ◽  
Xuyan Liu ◽  
Chongnian Qu ◽  
...  
Keyword(s):  
Band Gap ◽  
Design Method ◽  
Influence Factors ◽  
Low Frequency ◽  
Flexural Vibration ◽  
Band Gaps ◽  
Geometrical Parameters ◽  
Vibration Band ◽  
Bending Vibration ◽  
Elastic Metamaterials

This paper presents the modeling technique, design method, a new working way and influence factors for elastic metamaterial plates. Two kinds of new elastic metamaterials plates with local resonators are designed. The band structure and transmission spectrum are calculated by finite element method (FEM). The formation mechanism of the bending vibration band gap is further analyzed by the displacement field of the band gap and the dynamic effective dislocation density of the metamaterial plate. Compared with regular shapes, irregular shapes of oscillators and rubber are easier to open bending band gaps. The effects of the geometrical parameters on the flexural vibration band gaps (FVBGs) are studied in detail. The related results can well confirm that the two novel types of local resonators illustrate the vibration characteristics of the two-degree-of-freedom system during the vibration, and two obvious FVBGs can be found in low frequency. The double-side metamaterial plates can broaden the width of FVBGs. The installation angles have no effect on the dispersion curves of the double-side metamaterial plates.

scholarly journals Phononic Band Gaps of Elastic Periodic Structures: A Homogenization Theory Study

2007 ◽  
Author(s):  
Ying-Hong Liu ◽  
Chien C. Chang ◽  
Ruey-Lin Chern ◽  
C. Chung Chang
Keyword(s):  
Elastic Constants ◽  
Periodic Structures ◽  
Mass Density ◽  
Density Ratio ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Homogenization Theory ◽  
Dominant Factor ◽  
Phononic Band Gaps

In this study, we investigate band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. The phononic crystals consist of arrays of different media embedded in a rubber or epoxy. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. The physical background of this observation is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry Γ.

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.

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