Design of vibration isolators by using the Bragg scattering and local resonance band gaps in a layered honeycomb meta-structure

Based on the finite element method (FEM), characteristics of the local resonance band gap and the Bragg scattering band gap of two periodically-distributed vibrator structures are studied. Conditions of original anti-resonance generation are theoretically derived. The original anti-resonance effect leads to localization of vibration. Factors which influence original anti-resonance band gap are analyzed. The band gap width and the mass ratio between two vibrators are closely correlated to each other. Results show that the original anti-resonance band gap has few influencing factors. In the locally resonant structure, the Bragg scattering band gap is found. The mass density of the elastic medium and the elasticity modulus have an important impact on the Bragg band gap. The coexistence of the two mechanisms makes the band gap larger. The band gap covered 90% of the low frequencies below 2000 Hz. All in all, the research could provide references for studying the low-frequency and broad band gap of phononic crystal.

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Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance

Journal of Applied Mechanics ◽

10.1115/1.4004592 ◽

2011 ◽

Vol 79 (1) ◽

Cited By ~ 132

Author(s):

Liao Liu ◽

Mahmoud I. Hussein

Keyword(s):

Wave Propagation ◽

Band Structure ◽

Band Gap ◽

Frequency Band ◽

Band Gaps ◽

Flexural Wave ◽

Propagation Mechanism ◽

Bragg Scattering ◽

Frequency Spectra ◽

Local Resonance

Band gaps appear in the frequency spectra of periodic materials and structures. In this work we examine flexural wave propagation in beams and investigate the effects of the various types and properties of periodicity on the frequency band structure, especially the location and width of band gaps. We consider periodicities involving the repeated spatial variation of material, geometry, boundary and/or suspended mass along the span of a beam. In our formulation, we implement Bloch’s theorem for elastic wave propagation and utilize Timoshenko beam theory for the kinematical description of the underlying flexural motion. For the calculation of the frequency band structure we use the transfer matrix method, derived here in generalized form to enable separate or combined consideration of the different types of periodicity. Our results provide band-gap maps as a function of the type and properties of periodicity, and as a prime focus we identify and mathematically characterize the condition for the transition between Bragg scattering and local resonance, each being a unique wave propagation mechanism, and show the effects of this transition on the lowest band gap. The analysis presented can be extended to multi-dimensional phononic crystals and acoustic metamaterials.

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the Interaction of Resonance And Bragg Scattering Effects for the Locally Resonant Phononic Crystal with Alternating Elastic and Fluid Matrices

Archives of Acoustics ◽

10.1515/aoa-2017-0075 ◽

2017 ◽

Vol 42 (4) ◽

pp. 725-733 ◽

Cited By ~ 4

Author(s):

Bo Yuan ◽

Yong Chen ◽

Min Jiang ◽

Shuai Tang ◽

Miao He ◽

...

Keyword(s):

Phononic Crystal ◽

Three Dimensional ◽

Band Gaps ◽

Acoustic Properties ◽

Bragg Scattering ◽

Wavelength Band ◽

Local Resonance ◽

Scattering Effects ◽

Acoustic Speed ◽

Sub Wavelength

Abstract Three-dimensional (3D) locally resonant phononic crystals (LRPCs) are studied with the aim of optimising the sub-wavelength band gaps of such composites. By analysing their effective acoustic properties, it has been found that the effective acoustic speed of the composite will drop to zero when local resonance arise, and will increase monotonically when Bragg scattering effects occur. Moreover, if the matrix is a low-shear-speed medium, local resonators can significantly reduce the effective acoustic speed of the composite and, therefore, lower the frequency where Bragg scattering effects occur. Hence, a specific LRPC with alternating elastic and fluid matrices is proposed, whose resonance and Bragg gaps are already close in frequency. The fluid matrix behaves as a wave filter, which prevents the shear waves from propagating in the composite. By using the layer-multiple-scattering theory, the coupling behaviour of local resonance and Bragg scattering band gaps has been investigated. Both gaps are enhanced when they move closer to each other. Finally, a gap-coupled case is obtained that displays a broad sub-wavelength band gap. Such proposal excels at the application of underwater acoustic materials since the arrangement of structure can be handily adjusted for tuning the frequency of coupled gap.

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Widening, transition and coalescence of local resonance band gaps in multi-resonator acoustic metamaterials: From unit cells to finite chains

Journal of Sound and Vibration ◽

10.1016/j.jsv.2021.116716 ◽

2022 ◽

pp. 116716

Author(s):

A. Stein ◽

M. Nouh ◽

T. Singh

Keyword(s):

Band Gaps ◽

Acoustic Metamaterials ◽

Local Resonance ◽

Resonance Band ◽

Unit Cells

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Formation of local resonance band gaps in finite acoustic metamaterials: A closed-form transfer function model

Journal of Sound and Vibration ◽

10.1016/j.jsv.2017.08.009 ◽

2017 ◽

Vol 410 ◽

pp. 429-446 ◽

Cited By ~ 22

Author(s):

H. Al Ba'ba'a ◽

M. Nouh ◽

T. Singh

Keyword(s):

Transfer Function ◽

Closed Form ◽

Band Gaps ◽

Transfer Function Model ◽

Acoustic Metamaterials ◽

Function Model ◽

Local Resonance ◽

Resonance Band

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Insertion loss of periodic cylindrical shells with helical slit

Noise Control Engineering Journal ◽

10.3397/1/376920 ◽

2021 ◽

Vol 69 (3) ◽

pp. 199-208

Author(s):

Karisma Mohapatra ◽

Dibya Prakash Jena

Keyword(s):

Band Structure ◽

Insertion Loss ◽

Cylindrical Shells ◽

Slit Width ◽

Sharp Peak ◽

Acoustic Attenuation ◽

High Frequencies ◽

Local Resonance ◽

Resonance Band

We propose periodic shells with helical slit to overcome the lacuna in periodic C scatterers, where the first Bragg band is considerably reduced on increasing width of the slit. The key discovery of this research indicates that, by changing the upright slit of the C scatterers to helical slits, larger insertion loss (IL) is achieved around the first Bragg band without compromising the local resonance band. Comparing the performance of periodic shells without slit or cylindrical scatterers, it is found that IL becomes larger at first Bragg band. The pitch, thickness of the shell and width of helical slit can be altered to adjust the resonance of the proposed shells. On decreasing the pitch or increasing the slit width, the resonance band shifts toward high frequencies without much alteration in acoustic attenuation of bandwidth. Additionally, below threshold pitch, the said peak merges with first Bragg band and broadens with prominent IL. The calculated band structure authenticates the bandwidth of the first Bragg band, and the additional sharp peak in IL can be attributed to local resonance of the periodic scatterers.

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