Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals

Based on a better understanding of the lattice vibration modes, two simple spring-mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of the ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight into the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps in the ternary locally resonant phononic crystals. The analytical evaluations with our models and the theoretical predictions with the lumped-mass method are in good agreement with each other. The newly proposed heuristic models are helpful for a better understanding of the locally resonant band gap mechanism, as well as more accurate evaluation of the band edge frequencies.

Formation mechanism of the low-frequency locally resonant band gap in the two-dimensional ternary phononic crystals

The low-frequency band gap and the corresponding vibration modes in two-dimensional ternary locally resonant phononic crystals are restudied successfully with the lumped-mass method. Compared with the work of C. Goffaux and J. Sánchez-Dehesa （Phys. Rev. B 67 14 4301（2003））, it is shown that there exists an error of about 50% in their calculated results of the band structure, and one band is missing in their results. Moreover, the in-plane modes shown in their paper are improper, which results in the wrong conclusion on the mechanism of the ternary locally resonant phononic crystals. Based on the lumped-mass method and better description of the vibration modes according to the band gaps, the locally resonant mechanism in forming the subfrequency gaps is thoroughly analysed. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap is also verified in this ternary case.

Propagation Characteristics of Flexural Wave in One-Dimensional Phononic Crystals Based on Lattice Dynamics Model

In this paper, we establish discrete flexural lattice chain models of Bragg and locally resonant phononic crystals by setting mass defect atoms and local resonant elements on the flexural lattice chain. The bandgap characteristics of flexural wave in phononic crystals are studied by establishing the governing equations of the model. The results from models show that with the change of the mass ratio of defective atoms to normal atoms, the bandgap of the flexural wave produced by Bragg scattering shows a certain rule. When the local resonant bandgap and Bragg scattering bandgap are close to each other, the two bandgaps will be coupled to form a wider flexural wave bandgap. The effect of axial strain on bending wave propagation is only the shift of bandgap position. The effect of material damping on the propagation of a bending wave is only energy dissipation at high frequency. In addition, we use finite element simulation to calculate the bandgap of flexural wave in phononic crystals with mass defects, and the results are consistent with lattice chain model. This shows that lattice chain model can effectively guide the bandgap design of phononic crystals. This comprehensive study may help to elucidate the rule of bandgap generation of flexural wave in one-dimensional phononic crystals.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

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.

沙漏型声子晶体的中低频隔声减振性能研究

针对机械工业装备上难以解决的低频振动与噪声问题,提出一种小尺寸、轻量化的新型声子晶体结构,研究其隔声减振特性,通过有限元仿真计算该声子晶体无限周期排列时的隔声量、能带结构以及有限周期排列时的振动响应,分析该结构的隔声机理及减振特性,并研究了关键几何参数、散射体材料和声波入射角度对该结构的隔声特性的影响规律,以及板结构减振频带的拓宽方法.结果表明:该声子晶体结构在1 000 Hz以下频率范围内具有优越的隔声减振性能,通过将不同参数的结构进行组合的方法可以拓宽声子晶体板的减振频带,为工程结构的中低频隔声减振及声子晶体的应用提供了新的思路与可行性参考.

多重谐振水泥基声子晶体带隙特性研究

为了拓宽混凝土超材料弹性波衰减带的范围,本工作基于局域共振理论提出了一种多重谐振水泥基声子晶体。利用有限元方法,计算了多重谐振水泥基声子晶体的能带结构、本征模态和衰减特性,研究了带隙产生机理和影响因素,根据质量-弹簧系统推导了带隙估计式,分析了混凝土超材料充填层结构的减振性能。结果表明:多重谐振水泥基声子晶体在1~400 Hz频段内具有两个带隙,其中带隙的起始和截止频率由散射体Ⅰ、散射体Ⅱ和水泥砂浆基体的振动模式决定;包裹层的弹性模量、泊松比以及厚度是影响带隙的主要因素;由多重谐振水泥基声子晶体组成的混凝土超材料充填层结构在1~400 Hz频段内的加速度级均小于普通自密实混凝土充填层结构,特别是在带隙频段范围内振动降低了6~9 dB。

复合柱局域共振声子晶体的超宽带隙与可调性研究

局域共振声子晶体因具有良好的低频带隙特性,在低频减振降噪方面具有广泛的应用前景。以设计一种具有超宽带隙的三组元二维复合柱声子晶体结构为目标,该结构由散射体、双包覆层和六棱柱基体板组成,相对应的局域共振单元附加质量比为65.13,利用有限元方法计算该声子晶体板的能带结构、传输损失谱和位移矢量场。结果表明:在0~3000 Hz的频率范围内相对带宽高达162.10%。与方形柱基体板声子晶体相比,所设计的六棱柱基体板声子晶体的第一完全带隙频率更低且第二带隙频率范围更宽。通过优化几何结构、改变材料参数以及引入压电效应等方式,实现对多条完全带隙的调控,并进一步拓宽完全带隙形成超宽带隙。研究结果可为研发可调低频减振降噪产品提供一定的理论参考。

圆柱空腔橡胶层局域共振声子晶体双层板减振特性分析

针对机械设备中的低频减振问题,提出一种圆柱空腔橡胶层局域共振声子晶体双层板结构,即在双层板间周期性排列具有圆柱空腔的橡胶层和实心散射体振子。首先结合弹性波理论和BLOCH定理,采用有限元方法计算带隙范围并分析弯曲波带隙形成的原理,其次通过单变量和组合变量的方式分析单元参数对带隙的影响规律并依此对单元参数进行调整,使其弯曲波带隙范围为48.52~206.21 Hz,最后通过振动传输特性仿真验证其对弯曲波振动的减振效果。研究表明,圆柱空腔橡胶层双层板式声子晶体可以产生200 Hz以下的弯曲波带隙,且可以通过调整单元参数来使其匹配目标减振频段。声子晶体板的振动传输特性分析和振动位移图验证了其对带隙范围内弯曲波传输的抑制作用,可为基于声子晶体减振的工程应用提供一定的参考。

轴对称低频局域共振声子晶体带隙分析及优化

本文提出了一种新型轴对称Helmholtz声子晶体(AHPC),并对其进行了深入研究。通过建立数值模型,获取了AHPC结构的完整带隙,揭示了其带隙形成机理,描述了带隙边缘的声压分布特性,并通过实验获取了低频带隙,验证了数值模型的准确性。本文定量化地研究了颈部长度、颈部宽度和腔体长度对低频带隙宽度和带隙边缘频率的影响,明确了这三个参数是影响带隙分布的主要因素。其中颈部长度、腔体长度与带隙宽度正相关,与带隙边缘频率负相关,颈部宽度与带隙宽度和带隙边缘频率均呈正相关。基于Box-Behnken模型进行了响应面分析,得到了带隙宽度和带隙下限与三因素值间的函数关系。基于已获得的函数表达式,采用内点法对结构参数进行了优化,并通过数值模拟验证了优化结果,得到了具有298.49~519.27 Hz低频带隙的最优AHPC结构。

基于局域共振型声子晶体点缺陷态特性的低频振动能量回收研究

针对环境中广泛存在的低频振动控制问题,设计了一种二维三组元的新型局域共振型声子晶体结构。将完美声子晶体结构中一个单胞替换为压电材料以形成点缺陷结构,利用有限元方法对缺陷带的能量局域化特性进行了仿真研究,并探究了超胞大小和缺陷位置对能量回收性能的影响。研究表明,在能量回收系统中引入局域共振型声子晶体结构,可以显著提高系统的能量回收性能;当超胞结构的大小满足足够的周期性时,利用缺陷态回收的振动能量逐渐趋于稳定并达到最大值;在给定的超胞结构中,存在一个最优的缺陷位置,使得系统的振动能量回收性能达到最佳。对于最优的5×7超胞结构,在252.9 Hz处产生的最大峰-峰值电压为243.5 mV,是相同大小的环氧树脂裸板结构在同一频率处产生的输出电压0.64 mV的380倍。该研究结果可为低频弹性波的调控和解决低功耗仪器的自供电提供理论参考。

面向目标频率的声学超结构带隙优化设计研究

本文对悬臂梁式局域共振声子晶体的带隙特性进行研究,并提出一种通用的带隙优化设计方法。首先,分析声子晶体的带隙结构和形成机理,发现模态有效质量占比是带隙能否打开的关键因素。其次,基于响应面法对声子晶体的带隙进行优化设计研究,借助参数相关性分析筛选出关键的设计变量,通过最优空间填充设计获取试验点,构建响应面模型进行多目标优化,从而获得能够匹配特定目标频率的带隙优化设计方案。最后,对提出的优化方案进行验证。结果显示,优化后的局域共振单元2条带隙均在目标频率处打开。本研究成果可为局域共振型声子晶体的带隙优化设计提供一种方法和思路。

Research Progress of Underwater Soundabsorbing Material

This article provides an overview of underwater sound-absorbing materials mainly applied with polyurethane matrix.It mainly elaborates on the underwater sound mecha-nism,commonly used underwater sound-absorbing materials and structures,as well as new underwater sound-absorbing material structures derived from local resonance pho-nonic crystals,such as phononic crystals,local resonance phonon wood piles,and meta-material sound-absorbing structures.This provides a broader development space and direction for the future development of underwater sound-absorbing materials.

细直梁弯曲振动中的局域共振带隙

通过将声子晶体中的局域共振思想引入到细直梁的结构设计中,构造了一种具有低频局域共振带隙的周期结构细直梁。采用传递矩阵法计算了周期边界条件下该细直梁弯曲振动中的弹性波能带结构,计算结果表明该结构中存在低频弯曲振动带隙。采用有限元法计算了有限周期该细直梁的振动传输特性。以有机玻璃、橡胶/铜块振子构成的该局域共振细直梁为例,采用振动试验方法对其振动传输特性进行了测试。试验结果同理论及仿真结果相吻合。结果表明,局域共振结构可大大降低带隙频率,并增大带隙衰减。梁类结构是噪声及振动控制领域研究的主要对象之一,局域共振结构的应用为其提供了一种新的思路。

螺旋局域共振单元声子晶体板结构的低频振动带隙特性研究

低频振动和噪声的控制问题是当今环境面临的重要挑战。基于声子晶体的局域共振机理,设计一种新型的螺旋局域共振单元声子晶体板结构,并结合数值计算和试验测试对结构的低频振动带隙特性进行分析和验证。分析发现,共振带隙的产生是由螺旋共振单元的局域共振模态与板中传播的弹性波相互耦合作用造成的,而且带隙宽度与耦合强度直接相关。通过改变结构的材料和尺寸参数可以将共振带隙调节到满足实际应用要求的低频范围。数值计算结果与试验测试结果基本一致,同时证实所设计的结构在250 Hz以下的低频范围具有较宽的振动带隙,最低带隙频率低至42 Hz。这种结构设计及其研究结果为声子晶体研究提供了获得低频振动带隙的理论依据和有效方法,在低频减振降噪方面具有潜在的应用前景。

声子晶体禁带特性及局域共振现象的试验研究

以弹性(亚克力柱/空气型)及粘弹性(硅橡胶/空气型)声子晶体为研究对象,研究了散射体填充率、形状、排列方式、材料性质、缺陷形式等对声子晶体禁带特性及局域共振现象的影响。结果表明:随着层数的增加,带隙频率逐渐靠近理论值,但达到一定层数后,其影响会减弱;与正方柱形比较,圆柱形声子晶体得到的带隙更宽,而与弹性声子晶体相比,粘弹性声子晶体更易得到低频宽带隙的效果;声子晶体晶体阵列个数对共振频率的影响并不大,而散射体形状、填充率、及材料性质对共振频率有一定影响,尤其是粘弹性材料对提高局域共振的品质因子有非常大的作用;多点缺陷的引入对缺陷局域模态的分离有一定贡献,但多点缺陷间隔较近时会降低局域模态的分离效果。

基于质量放大局域共振型声子晶体的低频减振设计

针对低频结构振动控制,设计了一种质量放大局域共振型声子晶体。基于周期结构的Bloch定理和有限元方法研究了无限声子晶体的能带特性,同时基于有限元法研究了弹性波在有限周期结构中的传播特性。在此基础上,对声子晶体质量放大带隙与局域共振带隙的形成机理和带隙特性进行了研究。最后以梁框架结构低频减振为目标,将设计的质量放大局域共振声子晶体嵌入框架结构中,综合应用声子晶体带隙特性和黏弹性材料阻尼特性,实现低频宽带振动抑制效果。进一步,对框架结构一阶固有频率,进行声子晶体结构优化设计,实现了一阶固有频率处振动的高量级抑制,并设计制备实验样件,进行实验验证。结果表明,这种质量放大局域共振声子晶体可以为结构低频减振提供一种新的实现方法。

圆管型局域共振声子晶体三维构型振动带隙研究

采用多重多级子结构方法计算具有一定刚度的圆管型局域共振声子晶体三维构型振动带隙特性。考察包裹方向对带隙特性的影响,并对第一带隙上下边界点的单胞振动形式进行分析。结果表明,两种包裹形式都可以得到较低较宽的第一带隙,并且带隙特性相似,因而其周期结构都可以大幅减弱带隙范围内弹性波的传播。但两种构型带隙上下边界点对应振动形式不同,此外带隙特性还受单胞尺寸的影响。通过给定评价指标得到相关材料参数与带隙特性关系的相图,由此分析包裹层材料属性对带隙特性的影响。

具有压电分流电路的声子晶体杆振动带隙研究

压电分流电路的电磁振荡可以使声子晶体杆产生局域共振带隙。分析了杆局域共振带隙的形成机理,运用传递矩阵法计算了杆的带隙结构,并对分流电路中电感、电容和电阻对局域共振带隙的影响进行了研究。压电分流电路的电磁振荡可以使压电片的等效弹性模量变为负值,从而使贴有压电片梁的弹性模量减小,当弹性模量实部等于零时,振动无法在杆中传播,形成局域共振带隙。通过改变分流电路中电感和电容参数可以方便的调节局域共振带隙的位置,为声子晶体带隙的主动控制提供一种新的方法。

基于声子晶体及其缺陷态特性的车内降噪方法

为了抑制车内中低频噪声,运用板件声学贡献法分析了车身顶棚不同区域板件的振动对车内噪声的贡献,在贡献较大的区域设计了具有双带隙和点缺陷的声子晶体结构。利用双振子声子晶体的双重局域共振带隙特性降低正贡献区域噪声,同时点缺陷带隙特性避免负贡献区振动的衰减。结果表明,设计的声子晶体结构对降低车内噪声具有良好的效果。