周期多孔板的面内振动衰减域及其优化

针对Bragg散射型周期多孔板难以实现较低起始频率并维持较宽衰减域的问题,优化设计了一种含菱形孔的周期多孔板。采用有限元法结合周期边界条件,并运用COMSOL对周期多孔板的面内弹性波频散关系进行计算,通过ANSYS模拟有限尺寸周期多孔板的频率响应,将周期多孔板悬吊进行了正弦波激励的振动试验。研究结果表明,含菱形孔的周期多孔板相比于含圆形和六边形孔的周期多孔板具有更宽的衰减域;材料属性对衰减域影响较大,丁晴橡胶和硅橡胶易于获得低频衰减域;孔隙率的增大有利于获得低频宽带的衰减域;增大菱形孔水平夹角能获得较宽的衰减域。对衰减域的形成机理分析发现,含菱形孔的周期多孔板同时具有Bragg散射型和局域共振型声子晶体的特性,表明两种衰减域机理具有内在的联系。优化设计的周期多孔板存在一条5281.76 Hz至8824.30 Hz的完全衰减域,经过至少2个周期,振动即得到较明显衰减。数值和试验得到的衰减区具有较高的一致性。该研究为减振降噪板的开发提供了新的思路,且由于制作过程便捷,在改善建筑声环境中具有潜在的应用前景。      

Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases. The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.     

Flexural vibration of perforated plates and porous elastic materials under acoustic loading

This paper presents a method of theoretical treatment of acoustic coupling due to flexural vibration of perforated plates and plates of porous elastic materials. The analytical model is developed by introducing flow continuity at the plate surface in a spatially mean sense and air-solid interaction within the plate material. To demonstrate the method of application, some fundamental acoustic problems based on a classical thin-plate theory are analyzed and discussed in relation to the interactive effect of flexural vibration and plate permeability. For acoustic radiation from a vibrating plate excited by a harmonic point-force, the attenuation effect of power radiation appears at frequencies below the critical frequency of coincidence. In the problem of sound absorption of a perforated plate or a plate of porous elastic material backed by an air layer, as permeability decreases, the effect of plate vibration increases. For perforated absorber systems including plate vibration effects, the trend of variation from ordinary theory depends on plate thickness.     

How diffraction limits ultrasonic screening in phononic plate composed of a periodic array of resonant slits

We explore experimentally the role played by diffraction in the phenomenon of acoustic shielding provided by a plate that is periodically perforated with subwavelength slits and immersed in water. We carried out ultrasonic transmission measurements for all directions of propagation in order to check the omnidirectionality of acoustic shielding. While a single slit acts as a Fabry–Perot resonator in the frequency range of interest, the coupling between adjacent slits provides an attenuation frequency band centered around the resonant frequency that is mostly independent of the angle of incidence. Beyond the incident angle of 45 degrees, however, we observe the appearance of scattered radiation that limits the attenuation of ultrasound. This spurious scattering is shown to arise from diffraction by the grating of slits.     

Lamb wave band gaps in locally resonant phononic crystal strip waveguides

Using finite element method, we have made a theoretically study of the band structure of Lamb wave in a locally resonant phononic crystal strip waveguide with periodic soft rubber attached on the two sides of epoxy main plate. The numerical results show that the Lamb wave band gap based on local resonant mechanism can be opened up in the stub strip waveguides, and the width of the local resonant band gap is narrower than that based on the Bragg scattering mechanism. The results also show that the stub shape and width have influence on the frequency and width of the Lamb wave band gap.     

基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼     

Numerical Study of Air Flow Induced by Shock Impact on an Array of Perforated Plates

This study is focused on the propagation behavior and attenuation characteristics of a planar incident shock wave when propagating through an array of perforated plates. Based on a density-based coupled explicit algorithm, combined with a third-order MUSCL scheme and the Roe averaged flux difference splitting method, the Navier–Stokes equations and the realizable k-ε turbulence model equations describing the air flow are numerically solved. The evolution of the dynamic wave and ring vortex systems is effectively captured and analyzed. The influence of incident shock Mach number, perforated-plate porosity, and plate number on the propagation and attenuation of the shock wave was studied by using pressure- and entropy-based attenuation rates. The results indicate that the reflection, diffraction, transmission, and interference behaviors of the leading shock wave and the superimposed effects due to the trailing secondary shock wave are the main reasons that cause the intensity of the leading shock wave to experience a complex process consisting of attenuation, local enhancement, attenuation, enhancement, and attenuation. The reflected shock interactions with transmitted shock induced ring vortices and jets lead to the deformation and local intensification of the shock wave. The formation of nearly steady jets following the array of perforated plates is attributed to the generation of an oscillation chamber for the inside dynamic wave system between two perforated plates. The vorticity diffusion, merging and splitting of vortex cores dissipate the wave energy. Furthermore, the leading transmitted shock wave attenuates more significantly whereas the reflected shock wave from the first plate of the array attenuates less significantly as the shock Mach number increases. The increase in the porosity weakens the suppression effects on the leading shock wave while increases the attenuation rate of the reflected shock wave. The first perforated plate in the array plays a major role in the attenuation of the shock wave.     

Noise control by sonic crystal barriers made of recycled materials

A systematic study of noise barriers based on sonic crystals made of cylinders that use recycled materials like absorbing component is reported here. The barriers consist of only three rows of perforated metal shells filled with rubber crumb. Measurements of reflectance and transmittance by these barriers are reported. Their attenuation properties result from a combination of sound absorption by the rubber crumb and reflection by the periodic distribution of scatterers. It is concluded that the porous cylinders can be used as building blocks whose physical parameters can be optimized in order to design efficient barriers adapted to different noisy environments.     

ON THE ACOUSTIC ABSORPTION OF MULTI-LAYER ABSORBERS WITH DIFFERENT INNER STRUCTURES

A rigorous finite element analysis procedure is developed to study the effect of the inner structures on the acoustic absorption of multi-layer absorbers. To do this, four types of basic inner structure compartments adopted in the multi-layer absorbers are selected for analysis. These compartments are composed of porous materials inlaid with perforated plates of various shapes, say, triangle, semicircle, convex rectangle and plate shapes. As it is different from the conventional finite element analysis for the acoustic system in the literature, the perforated plates are simulated by appropriate equivalent boundary conditions, depending on their thickness, hole radius, hole pitch and porosity and the air contained in the holes. A large number of total degrees of freedom generated from meshing the air in the holes of perforated plates are thus avoided. The results reveal that the inner structures of the multi-layer absorbers will influence the acoustic absorption at some frequency bands significantly. Based on those features, the multi-layer absorber with a novel inner structure is then designed and manufactured. Both the finite element and experimental results show that its acoustic absorption would be distinctly promoted.     

Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex

It is common for dispersion curves of damped periodic materials to be based on real frequencies as a function of complex wavenumbers or, conversely, real wavenumbers as a function of complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained.     

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.     

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.     

Transverse mode competition in defect states of a waveguide with corrugated walls

We investigate the defect states arising in the Bragg and non-Bragg gaps by inserting a straight duct into a waveguide with periodically corrugated walls. In periodic waveguides, the Bragg gap is created by the interference of the same transverse modes whereas the different mode coupling leads to the non-Bragg one. Due to the involved high-order modes, there are two defect states observed in the non-Bragg gap while only one in the Bragg gap, indicating that transverse modes play a significant role in the creation of defect states. Furthermore, the frequency of each defect state highly relies on the defect geometries and their band widths can be optimized by the number of waveguide segments. The proposed transverse mode competition analysis reveals the mechanism of frequency shifting and provides an opportunity for guided wave control engineering, which would definitely benefit their applications in various functional devices, such as filters, sensors, and amplifiers.     

Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals

We study the propagation of thickness-twist (TT) waves in a crystal plate of AT-cut quartz with periodically varying, piecewise constant thickness. The scalar differential equation by Tiersten and Smythe is employed. The problem is found to be mathematically equivalent to the motion of an electron in a periodic potential field governed by Schrodinger’s equation. An analytical solution is obtained. Numerical results show that the eigenvalue (frequency) spectrum of the waves has a band structure with allowed and forbidden bands. Therefore, for TT waves, plates with periodically varying thickness can be considered as phononic crystals. The effects of various parameters on the frequency spectrum are examined.     

二维空心散射体声子晶体板的低频带隙特性及其形成机理

利用有限元方法,对设计的涂有硅橡胶包裹层的空心铅柱体嵌入到4个环氧树脂短连接板中构成的声子晶体板的低频带隙特性进行了研究,分析了其能带结构、传输损失及位移场。与正方连接板粘连结构、嵌入结构和细连接短板粘连结构这3种传统声子晶体板的带隙特性作对比,说明具有包裹层、短连接板结构的声子晶体板更容易产生低频宽带;观察位移矢量场的振动模态,并结合弹簧质量模型,解释了带隙形成的机理;通过讨论连接板的宽度、散射体的内外半径及高度对第一完全带隙的影响,说明连接板宽度越窄,厚度越小,散射体内半径越小,外半径越大,高度越高,越有利于带隙的扩展。      

Panel of resonators with variable resonance frequency for noise control

The article focuses on acoustic resonators made of perforated sheets bonded onto honeycomb cavities. This kind of resonators can be used in adverse conditions such as high temperature, dirt and mechanical constraints. For all these reasons, they are, for example, widely used in aeronautic applications. The acoustic properties are directly linked to the size, shape and porosity of holes and to the thickness of air gaps. Unfortunately, the acoustic absorption of these resonators is selective in frequency and conventional acoustic resonators are only well adapted to tonal noises. In case of variable tonal noise, the efficiency is limited if the resonators are not tunable. One common solution is to control the depth of cavities based on the noise to be attenuated. This article proposes another technology of tunable resonators with only a very small mass and size increase. It consists of two superposed and identically perforated plates associated with cavities. One plate is fixed and bonded to the cavities and the other plate is mobile. The present concept enables to change the internal shapes of the holes of the perforated layers. The article describes this system and gives a theoretical model of the normal incidence acoustic impedance that allows to predict the acoustic behavior, in particular the resonance frequency. The model shows that the resonance frequency varies with hole profiles and that the absorption peak moves towards the lower frequencies. The proposed model is validated by measurements on various configurations of resonators tested in an impedance tube. The perspectives of this work are to adapt the hole profiles using an actuator in order to perform active control of impedance.     

Three-dimensional simulation of electric field and space charge in the advanced hybrid particulate collector

The advanced hybrid particulate collector (AHPC) is an efficient hybrid system that combines the electrostatic precipitator (ESP) and the bag filter in a unique approach. In this study, an unstructured finite volume method (FVM) is used to compute the three-dimensional distributions of the electric field and the space charge density in an AHPC setup for two cases: without the perforated plate and with the perforated plate. The current–voltage characteristics of the AHPC setup are measured. The current on the bag plate has a mean value 7.82 μA without the perforated plate and 0.08 μA with the perforated plate for the measured voltages. The total currents are used to calculate the charge density at the corona wire according to the Peek's formula. For both cases, the numerical predictions of the current–voltage relations of the plates of the model AHPC agree well with the measurements. When the AHPC has the perforated plate, numerical results show that the electric field and space charge density distributions on the perforated plate have the same number of peaks corresponding to the holes. The electric field on the bag plate surface is lower than that of the top plate and the perforated plate. Though the bag plate has low current, its surface still has high space charge density. When the AHPC has no perforated plate, the electric field is higher than six times and the space charge density is higher than three times that of the case with the perforated plate on the bag plate surface.     

Matryoshka locally resonant sonic crystal

The results of numerical modeling of sonic crystals with resonant array elements are reported. The investigated resonant elements include plain slotted cylinders as well as their various combinations, in particular, Russian doll or Matryoshka configurations. The acoustic band structure and transmission characteristics of such systems have been computed with the use of finite element methods. The general concept of a locally resonant sonic crystal is proposed that utilizes acoustic resonances to form additional band gaps that are decoupled from Bragg gaps. An existence of a separate attenuation mechanism associated with the resonant elements that increases performance in the lower frequency regime has been identified. The results show a formation of broad band gaps positioned significantly below the first Bragg frequency. For low frequency broadband attenuation, a most optimal configuration is the Matryoshka sonic crystal, where each scattering unit is composed of multiple concentric slotted cylinders. This system forms numerous gaps in the lower frequency regime, below Bragg bands, while maintaining a reduced crystal size viable for noise barrier technology. The finding opens alternative perspectives for the construction of sound barriers in the low frequency range usually inaccessible by traditional means including conventional sonic crystals.     

Plasmonic structure generation by laser illumination of silica colloid spheres deposited onto prepatterned polymer-bimetal films

Plasmonic structures are prepared on bimetal films evaporated onto glass substrates applying a multi-step process, and atomic force microscopy is utilized to study the structures after each step. Sub-micrometer gratings are generated on polycarbonate films spin-coated onto silver-gold bimetal layers by interference lithography (IL) applying the fourth harmonics of a Nd:YAG laser. These polymer gratings are used as prepatterned templates in order to deposit silica colloid spheres by spin-coating. It is shown that the conditions of periodic silica sphere-array formation along the template valleys are sufficiently large grating modulation depth, appropriate ratio of silica sphere diameter to grating period, and optimized speed of spinning. The periodic silica sphere arrays are illuminated by a homogeneous KrF excimer laser beam, and periodically arrayed sub-wavelength holes are drilled into bimetal films via colloid sphere lithography (CSL). The characteristic dimensions of the resulted plasmonic structures are defined by the polymer grating period and by the silica colloid sphere diameter. Attenuated total reflection spectroscopy is performed exciting plasmons on different metal-dielectric interfacial structures by the second harmonic of a continuous Nd:YAG laser. The polar and azimuthal angle dependent grating-coupling and scattering effects of the complex periodic structures on the resonance characteristic of plasmons is demonstrated.     

Scanning tunneling spectroscopy of Ag films: the effect of periodic versus quasiperiodic modulation

By using scanning tunneling spectroscopy to probe a silver thin film that contains both periodic and quasiperiodic modulation, and by using Fourier analysis, we unravel the influences of individual Fourier components of the scattering potential (periodic versus quasiperiodic) on the electronic structure of a one-dimensional quasiperiodically modulated thin Ag film. Along the periodically modulated direction, a Bragg reflection-induced energy gap is observed in k space. On the other hand, the exotic E vs k spectrum with many minigaps was observed along the quasiperiodic direction.