局域共振复合单元声子晶体结构的低频带隙特性研究

本文提出了一种新型局域共振复合单元声子晶体结构, 并结合有限元方法对结构的带隙机理及低频共振带隙特性进行了分析和研究. 共振带隙产生的频率位置由所对应的局域共振模态的固有频率决定, 并且带隙宽度与局域共振模态的品质因子及其与基体之间的耦合作用强度有关. 采用局域共振复合单元结构可以实现声子晶体的多重共振, 在低频范围能打开多条共振带隙, 但受到共振单元排列方式的的影响. 由于纵向和横向局域共振模态的简并, 复合单元结构能在200 Hz以下的低频范围打开超过60%宽度的共振带隙, 最低带隙频率低至18 Hz. 这为声子晶体结构获得低频、超低频带隙提供了一种有效的方法. 关键词： 局域共振 低频带隙 复合单元 声子晶体     

Manipulating sonic band gaps at will: vibrational density of states in three-dimensional acoustic metamaterial composites

Vibrational properties of elastic composites containing a mass-in-mass microstructure embedded in a solid matrix are numerically studied. Using a lattice model, we investigate the vibrational density of states in three-dimensional composite structures where resonant particles are randomly dispersed. By dispersing such particles in the system, a sonic band gap appears. It is confirmed that this band gap can be introduced in a desired frequency regime by changing the parameters of resonant particles and the frequency width of this band gap can be controlled by varying the concentration of the resonant particles to be dispersed. In addition, multiple sonic band gaps can be realized using different species of resonant particles. These results enable us to suggest an alternative method to fabricate devices that can inhibit the propagation of elastic waves with specific frequencies using acoustic metamaterials.     

Interplay of local resonances and Bragg band gaps in acoustic waveguides with periodic detuned resonators

This letter is concerned with acoustic wave propagation and transmission in acoustic waveguides with periodically grafted detuned Helmholtz resonators. The interplay of local resonances and Bragg band gaps in such periodic systems is examined. It is shown that, when the resonant frequencies of the resonators are tuned close to a Bragg band gap, the behavior of the Bragg band gap can be affected dramatically. Particularly, by introducing appropriately tuned resonators, the bandwidth of a Bragg band gap can be reduced to zero, leading to a very narrow pass band with great wave attenuation performance near both band edges. The band formation mechanisms of such periodic waveguides are further examined, providing explicit formulae to locate the band edge frequencies of all the band gaps, as well as the conditions to achieve very narrow pass bands in such periodic waveguides.     

A review on sonic crystal,its applications and numerical analysis techniques

This paper presents a review study on sonic crystal, their development and present status. The paper also focuses on some of the applications of sonic crystal and numerical methods to study these crystals. Sonic crystals are periodic arrangement of scatterers, whose interaction with acoustic waves leads to the formation of band gap. Band gap are regions of frequencies where the sound propagation is significantly restricted from the sonic crystal. This property is used in many applications such as sound barrier, frequency filter, acoustic imaging etc. The paper presents a review of all these applications. Further the paper presents some of the numerical methods used to calculate the band gap formation in sonic crystal.     

Broadband locally resonant beams containing multiple periodic arrays of attached resonators

The plane wave expansion method is extended to study the flexural wave propagation in locally resonant beams with multiple periodic arrays of attached spring-mass resonators. Complex Bloch wave vectors are calculated to quantify the wave attenuation performance of band gaps. It is shown that a locally resonant beam with multiple arrays of damped resonators can achieve much broader band gaps, at frequencies both below and around the Bragg condition, than a locally resonant beam with only a single array of resonators, although the two systems have the same total resonator masses.     

Modelling and simulation of acoustic wave propagation in locally resonant sonic materials

Sonic crystals are artificial structures consisting of a periodic array of acoustic scatterers embedded in a homogeneous matrix material, with a usually large impedance mismatch between the two materials. They exhibit strong sound attenuation at selective frequency bands due to the interference of multiply reflected waves. However, sound attenuation bands in the audible range are only achieved by unfunctionally large sonic crystals. If local resonators are used instead of simple scatterers, the frequencies of the attenuation bands can be reduced by about two orders of magnitude. In the present paper we perform numerical simulations of acoustic wave propagation through sonic crystals consisting of local resonators using the local interaction simulation approach (LISA). Three strong attenuation bands are found at frequencies between 0.3 and 6.0 kHz, which do not depend on the periodicity of the crystal. The results are in good qualitative agreement with experimental data. We analyze the dependence of the resonance frequencies on the structural parameters of the local resonators in order to create a tool for design and optimization of any kind of sonic crystal.     

Enhanced acoustic localization in the two-dimensional phononic crystals with slit tube defect

In this paper, the acoustic localization characteristics of the two-dimensional phononic crystals with slit tube defect are investigated theoretically and experimentally. In contrast to the typical formation pattern of defect states, the proposed defect states are created by replacing a slotted tube in the center of perfect phononic crystal. Compared to perfect phononic crystal, the proposed structure can effectively localize waves of specific frequencies in the point defect and improve the acoustic pressure amplification. Then the effects of the geometric parameters of the slotted tube on the acoustic localization characteristics are studied. Numerical results show that the resonant frequency and acoustic pressure amplification amplitude could be effectively modulated by the geometric parameters of the slotted tube. Experimental results are in good agreement with the simulation results.     

类蜂窝状结构完全带隙二维光子晶体

通过在二维三角晶格中引入两个完全一样的介质圆柱构成了类蜂窝状结构光子晶体,并对其光子能带进行了频域计算。借助数值方法分析了介质柱位置改变对光子能带的影响,计算结果表明,这种类蜂窝状结构二维光子晶体可以产生很宽的带隙,而且在一定填充率下,可以通过调整介质柱的位置使完全光子带隙达到最大化。     

Low frequency phononic band structures in two-dimensional arc-shaped phononic crystals

The low frequency phononic band structures of two-dimensional arc-shaped phononic crystals (APCs) were studied by the transfer matrix method in cylindrical coordinates. The results showed the first phononic band gaps (PBGs) of APCs from zero Hz with low modes. Locally resonant (LR) gaps were obtained with higher-order rotation symmetry, due to LR frequencies corresponding to the speeds of acoustic waves in the materials. These properties can be efficiently used in a structure for low frequencies that are forbidden, or in a device that permits a narrow window of frequencies.     

Quality enhancement and insertion loss reduction of a rectangular resonator by employing an ultra-wide band gap diamond phononic crystal

We report on an ‘in plane mode’ band gaps investigation of a novel diamond CRS (circle-rectangle-square) shaped holey phononic crystals in the desired operating frequency ranges. An ultra-wide band gap for diamond in the ‘in plane mode’ is observed. We also investigate an ultra-wide acoustic band gap for a finite one-dimensional (1D) diamond CRS phononic crystal (PnC) in the ‘out of plane mode’, and an ultra-wide acoustic band gap of a finite two-dimensional (2D) diamond CRS phononic crystal (PnC) in the ‘out of plane mode’ based on the FEA (Finite Element Analysis) method. We analyze that the transmission response of diamond in the length extension and width extension manner is more reasonable. Ultra-wide peak attenuations in the transmission spectra of a CRS shaped diamond phononic crystal successfully reveal the complete band gaps. The wide band gap of a CRS shaped diamond phononic crystal and the wide peak attenuation strongly agree in the same frequency region. It is analyzed that when a CRS-diamond phononic crystal is employed for MEMS resonators with different tether widths the quality Q of the resonators improved, and the energy losses decrease with extremely low insertion loss. In addition, it is observed that the vibrational displacement of a resonator is reduced by employing a diamond phononic crystal.     

Effect of the internal rib structure of the inclusions on the two-dimensional phononic crystal composed of periodic slotted tubes in air

Using a finite element method based on the Bloch theorem, a new phononic crystal composed of periodic slotted tubes with internal rib structure in air is investigated. Two parallel plates with slit are introduced into the inclusion as the internal rib structure and its effect on band gaps is studied. The band structure and acoustic modes of the PC are calculated. Results show that the starting frequency of the first band gap is rather lower than that of slotted tubes without rib structure. The internal rib structure plays an important role in both the lower and upper edges of the first band gap. Some rib structural parameters are also studied for their effects on the first band gap. Results show that the first gap can be modulated widely by these parameters and the Helmholtz resonator theory can be used to explain the relationship between the band gap and the parameters.     

Hybrid phononic crystal plates for lowering and widening acoustic band gaps

We propose hybrid phononic-crystal plates which are composed of periodic stepped pillars and periodic holes to lower and widen acoustic band gaps. The acoustic waves scattered simultaneously by the pillars and holes in a relevant frequency range can generate low and wide acoustic forbidden bands. We introduce an alternative double-sided arrangement of the periodic stepped pillars for an enlarged pillars’ head diameter in the hybrid structure and optimize the hole diameter to further lower and widen the acoustic band gaps. The lowering and widening effects are simultaneously achieved by reducing the frequencies of locally resonant pillar modes and prohibiting suitable frequency bands of propagating plate modes.     

Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators

A uniform string with periodically attached spring-mass resonators represents a simple locally resonant continuous elastic system whose band gap mechanisms are basic to more general and complicated problems. In this Letter, analytical models with explicit formulations are provided to understand the band gap mechanisms of such a system. Some interesting phenomena are demonstrated and discussed, such as asymmetric/symmetric attenuation behavior within a resonance gap, and the realization of a super-wide gap due to exact coupling between Bragg and resonance gaps. In addition, some approximate formulas for the evaluation of low frequency resonance gaps are derived using an approach different from existing investigations.     

Anomalous coherent backscattering of light from opal photonic crystals

We studied coherent backscattering (CBS) of light from opal photonic crystals with incomplete band gaps. We observed a dramatic broadening of the CBS cone for incident angles close to the Bragg condition in the crystals. We modify the conventional CBS theory to incorporate Bragg attenuation resulting from the photonic band structure. By fitting the CBS data with the modified theory, we extract both the disorder-induced light mean-free path and the Bragg attenuation length of the inherent opal photonic crystal.     

内插扩张室声子晶体管路带隙特性研究

声子晶体管路的带隙特性,可以实现管路系统在特定频率下的噪声控制.利用二维模态匹配法推导出单个内插扩张室元胞的传递矩阵,结合Bloch定理,得到声子晶体管路的能带结构计算方法;验证了二维方法在计算能带结构时的准确性.研究发现,内插扩张室声子晶体管路存在布拉格带隙和局域共振带隙.进一步研究了晶格常数以及内插管长度对能带结构的影响,结果表明,晶格常数主要控制布拉格带隙,而内插管长度对局域共振带隙有较大的影响,并研究了两种参数变化下的带隙耦合.研究结果可以为管路降噪设计提供新的思路.     

二维组合宽带隙材料的研究

运用FDTD(时域有限差分法)研究了弹性波/声波通过二维正方形排列的铁/水声子晶体的传播特性.发现铁/水声子晶体在高频范围存在完全带隙，软包层铁/水声子晶体在低频范围出现共振带隙，它们分别对应于不同的带隙形成机理.通过铁/水声子晶体和软包层铁/水声子晶体的组合，可以得到从高频到低频的组合宽带隙结构，从而达到在更宽频范围内控制弹性波传播的目的；而且通过调整包层的厚度、铁芯的大小、以及填充率等结构参数，可以有效地调节组合宽带隙的频率结构.     

Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid

Flexural vibration in a pipe system conveying fluid is studied. The pipe is designed using the idea of the phononic crystals. Using the transfer matrix method, the complex band structure of the flexural wave is calculated to investigate the gap frequency range and the vibration reduction in band gap. Gaps with Bragg scattering mechanism and locally resonant mechanism can exist in a piping system with fluid loading. The effects of various parameters on the gaps are considered. The existence of flexural vibration gaps in a periodic pipe with fluid loading lends new insight into the vibration control of pipe system.     

Band structure of a two-dimensional resonant photonic crystal

The band structure of two-dimensional resonant photonic crystals of two types has been calculated using the expansion of eigenfunctions in plane waves. Crystals of one type consist of infinite dielectric cylinders forming a square lattice filled with a resonant gas, and crystals of the other type consist of infinite cylindrical holes filled with a resonant gas and forming a square lattice in a dielectric matrix. It has been shown that, in both cases, the dispersion of a resonant gas in combination with the dispersion of a two-dimensional structure with a photonic band gap leads to the appearance of an additional narrow transmission band near the edge of the band gap or an additional band gap in the continuous spectrum of the photonic crystal. The calculations performed have demonstrated that new dispersion properties substantially depend on the density of the resonant gas, the position of the resonant frequency with respect to the edge of the band gap, and the direction of propagation of electromagnetic waves.     

Simultaneous occurrence of structure-directed and particle-resonance-induced phononic gaps in colloidal films

We report on the observation of two hypersonic phononic gaps of different nature in three-dimensional colloidal films of nanospheres using Brillouin light scattering. One is a Bragg gap occurring at the edge of the first Brillouin zone along a high-symmetry crystal direction. The other is a hybridization gap in crystalline and amorphous films, originating from the interaction of the band of quadrupole particle eigenmodes with the acoustic effective-medium band, and its frequency position compares well with the computed lowest eigenfrequency. Structural disorder eliminates the Bragg gap, while the hybridization gap is robust.