Two-dimensional ternary locally resonant phononic crystals with a comblike coating

Propagation of elastic waves in acoustic metamaterials based on locally resonant viscoelastic phononic crystals is discussed. A variational formulation of the complex band structure for in-plane polarized waves is proposed and used to formulate a finite element model. Two different types of locally resonant band gaps are found for quasilongitudinal and quasishear waves, with distinct features in terms of complex bands and transmission bandwidth. The influence of viscosity on the complex band structure, transmission properties, and effective dynamic mass density of two-dimensional locally resonant metamaterials is further investigated. It is found that bands that were degenerate in the elastic case are separated when viscosity is introduced, and that sharp corners at high symmetry points become rounded. Transmission is generally worsened in passing bands, while it is enhanced inside locally resonant band gaps, contrary to what was observed previously for Bragg band gaps. All changes in the complex band structure and transmission spectra are solely due to the dispersive and dissipative effects of viscosity. It is also found that the negative mass density property may also disappear when viscosity is introduced. These results are relevant to practical applications of elastic and viscoelastic metamaterials.

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“…The classical (real-valued) band structure of Ref. [38] is displayed in Fig. 2 with the solid line for visual comparison.…”

Section: Complex Band Structurementioning

confidence: 99%

Wave propagation in two-dimensional viscoelastic metamaterials

2015

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“…Wang et al have introduced the narrow slit structures into the inclusions of the two-dimensional PC structure composed of steel tubes in air and obtained large BGs in audible frequency range. Wang et al discussed the absolute band gap (ABG) structures in PCs with cross-like holes [8]. Liu et al designed a tree-component PC structure that exhibits BGs two orders of magnitude smaller than the relevant wavelength which proposed the localized resonance (LR) mechanism [9].…”

Section: Introductionmentioning

confidence: 99%

“…Yu et al studied 2DPCs with neck structures and obtained the large band gaps in the low frequency [15]. Wang et al also explained the ternary locally resonant PCs with a comb-like coating using "spring-mass" model [8].…”

Section: Introductionmentioning

confidence: 99%

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

Liu¹,

Li²,

Zhong³

et al. 2015

Shock and Vibration

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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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“…If the steel columns and Si-rubber between them in the dual-and triple-oscillator systems are considered as a whole, the vibration mode at the lower edge of the band gap in those systems can be simplified as a single-oscillator, massspring model-but because the dual-oscillator steel column is divided into two parts and the triple-oscillator steel column is divided into three parts, the vibration energy is concentrated in the central steel column so that the mass in the mass-spring simplified model decreases as the number of the oscillators increases. The effect of changes in spring stiffness coefficient is smaller compared to changes in mass, so (1) shows where the original frequency of the first band gap in the system increases as the number of oscillators increases. Acoustic wave propagation in solids can be explained from the perspective of the effective medium parameters [8].…”

Section: Comparison Of Three Acoustic Metamaterialsmentioning

confidence: 99%

“…Acoustic metamaterials possess certain peculiar acoustic characteristics that natural materials do not have (e.g., negative effective mass density, negative effective modulus) and as such have garnered considerable attention for their promise in applications such as acoustic/elastic filters, acoustic mirrors, and sound insulators/absorbers [1,2]. Acoustic metamaterials are usually composed of a series of periodically arranged resonance units [3].…”

Section: Introductionmentioning

confidence: 99%

Investigation on the Band Gap and Negative Properties of Concentric Ring Acoustic Metamaterial

Chen

Meng

Jiang

et al. 2018

Shock and Vibration

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The acoustic characteristics of 2D single-oscillator, dual-oscillator, and triple-oscillator acoustic metamaterials were investigated based on concentric ring structures using the finite element method. For the single-oscillator, dual-oscillator, and triple-oscillator models investigated here, the dipolar resonances of the scatterer always induce negative effective mass density, preventing waves from propagating in the structure, thus forming the band gap. As the number of oscillators increases, relative movements between the oscillators generate coupling effect; this increases the number of dipolar resonance modes, causes negative effective mass density in more frequency ranges, and increases the number of band gaps. It can be seen that the number of oscillators in the cell is closely related to the number of band gaps due to the coupling effect, when the filling rate is of a certain value.

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Two-dimensional ternary locally resonant phononic crystals with a comblike coating

Cited by 34 publications

References 12 publications

Wave propagation in two-dimensional viscoelastic metamaterials

Wave propagation in two-dimensional viscoelastic metamaterials

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

Investigation on the Band Gap and Negative Properties of Concentric Ring Acoustic Metamaterial

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