Band structures of elastic waves in two-dimensional eight-fold solid–solid quasi-periodic phononic crystals

Combined with the supercell method, band structures of the anti-plane and in-plane modes of two-dimensional （2D） eight-fold solid-solid quasi-periodic phononic crystals （QPNCs） are calculated by using the finite element method. The influences of the supercell on the band structure and the wave localization phenomenon are discussed based on the modal distributions. The reason for the appearance of unphysical bands is analyzed. The influence of the incidence angle on the transmission spectrum is also discussed.

Propagation behavior of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with line defects

Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional （1D） piezoelectric/piezomagnetic （PE/PM） phononic crystals （PCs） with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the re- placement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly de- pendent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures.

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.

Wavelet-based method for computing elastic band gaps of one-dimensional phononic crystals

A wavelet-based method was developed to compute elastic band gaps of one-dimensional phononic crystals. The wave field was expanded in the wavelet basis and an equivalent eigenvalue problem was derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method was then applied to a binary system. For comparison, the elastic band gaps of the same one-dimensional phononic crystals computed with the wavelet method and the well- known plane wave expansion (PWE) method are both presented in this paper. The numerical results of the two methods are in good agreement while the computation costs of the wavelet method are much lower than that of PWE method. In addition, the adaptability of wavelets makes the method possible for efficient band gap computation of more complex phononic structures.

Band structures of elastic SH waves in nanoscale multi-layered functionally graded phononic crystals with/without nonlocal interface imperfections by using a local RBF collocation method

A meshless radial basis function （RBF） collocation method based on the Eringen nonlocal elasticity theory is developed to calculate the band structures of ternary and quaternary nanoscale multi-layered phononic crystals （PNCs） with functionally graded （FG） interlayers. Detailed calculations are performed for anti-plane transverse waves propagating in such PNCs. The influences of FG and homogeneous interlayers, component number, nonlocal interface imperfections and nanoscale size on cut-off frequency and band structures are investigated in detail. Numerical results show that these factors have significant effects on band structures at the macroscopic and microscopic scales.

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

A boundary element method(BEM) is presented to compute the transmission spectra of two-dimensional(2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction.The cross sections of the scatterers may be circular or square.For a periodic cell,the boundary integral equations of the matrix and the scatterers are formulated.Substituting the periodic boundary conditions and the interface continuity conditions,a linear equation set is formed,from which the elastic wave transmission can be obtained.From the transmission spectra,the band gaps can be identified,which are compared with the band structures of the corresponding infinite systems.It is shown that generally the transmission spectra completely correspond to the band structures.In addition,the accuracy and the efficiency of the boundary element method are analyzed and discussed.

Band structure properties of elastic waves propagating in the nanoscaled nearly periodic layered phononic crystals

The localization factor is used to describe the band structures for P wave propagating normally in the nanoscaled nearly periodic layered phononic crystals. The localization factor is calculated by the transfer matrix method based on the nonlocal elastic continuum theory.Three kinds of nearly periodic arrangements are concerned, i.e., random disorder, quasiperiodicity and defects. The influences of randomly disordered degree of the sub-layer＇s thickness and mass density, the arrangement of quasi-periodicity and the location of defect on the band structures and cut-off frequency are analyzed in detail.

Study on the vibration band gap and vibration attenuation property of phononic crystals

Phononic crystals (PCs) are functional materials with periodic structures and elas- tic wave (vibration) band gaps, where propagation of vibrations with frequencies within band gaps is forbidden. PCs with finite periods can restrain the propagation of vibrations with frequencies in band gaps and thus has vibration attenuation property. Worldwide, many institutions and researchers are engaged in the re- search of PCs, however, studies on the vibration attenuation property of PCs are still limited. In this paper, we report our study of band gaps and vibration attenua- tion properties of 1) a simplified PC—periodic mass-spring structures, 2) longitu- dinal vibration of one-dimensional (1D-), 2D-, 3D-PCs, and 3) the flexural vibration of 1D- and 2D-PCs. These studies provide a foundation for the applications of PCs in vibration attenuation.

恒频声学二极管的设计及特性研究

声学二极管能控制声波仅在一个方向有效传输在反方向无法传播,在通信技术中具有广泛的应用,然而目前大多数的声学二极管设计是基于非线性效应使系统只通过新的高次频率并阻止原频率的传输.本文利用不对称结构与弱非线性声子晶体的组合,提出了一种一维声二极管模型,实现弹性波的不对称传输,并保持频率不变.该模型由左端的变幅杆和右端的非线性弹簧质量链组成,理论分析表明,该声学二极管具有与电子二极管相同的正向和反向特性,并通过有限元仿真验证了该模型的有效性.

弹性支撑条件下声子晶体角梁结构振动特性分析研究

为了进一步探究一维声子晶体结构的振动特性,本文开展了弹性支撑条件下一维声子晶体角梁结构弯曲位移的振动特性研究。通过采用有限元分析法,分别对L型和T型声子晶体角梁结构进行模型建立,并对频率范围内的弯曲位移响应曲线进行绘制。同时,对弹性支撑条件、晶格长度、组分比、连接角度以及弹性支撑刚度对不同类型声子晶体角梁结构的带隙影响规律进行了研究。结果表明,弹性支撑刚度对声子晶体角梁结构的第一带隙有着明显的影响。

周期结构细直梁弯曲振动中的振动带隙

通过将声子晶体中的周期结构思想引入到细直梁的结构设计中,构造了一种二组元变截面周期结构细直梁。采用平面波展开法计算了无限周期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,在该细直梁中存在振动带隙。晶格尺寸、材料组分比、截面尺寸对振动带隙的影响也进行了讨论。采用有限元法计算了有限周期的细直梁的振动传输特性,计算得到的振动传输特性曲线上的频率衰减范围与平面波计算得到的带隙位置基本吻合。最后以有机玻璃及铝构成的细直梁为例,采用振动试验对其振动传输特性进行了测试。试验结果同理论计算及仿真结果基本吻合。梁类结构是噪声及振动控制领域研究的主要对象之一,周期结构细直梁中存在弯曲振动带隙为梁类结构的减振提供了一种新的思路。

声学超材料在低频减振降噪中的应用评述

低频机械波在传播过程中穿透力强,难以衰减,特别是次声频段的机械波易与机体器官发生共振,对身体造成危害。为了实现对低频机械波的有效控制,解决现代工业生产和生活中普遍存在的噪声污染问题,结合最近十几年发展起来的声子晶体和声学超材料,系统地总结和论述通过声子晶体和声学超材料解决低频振动噪声问题的新方法。归纳和总结典型的低频振动噪声来源和对其进行控制方面存在的一些困难,介绍低频振动噪声的危害。重点概括基于声子晶体禁带特性实现低频振动噪声被动控制的相关研究工作,主要介绍通过亚波长尺寸特征的杆、薄板和薄膜类结构来实现低频振动和噪声衰减的具体方法和效果。在声学超材料的理论框架下,讨论薄膜类结构在低频振动噪声衰减中的应用及其优缺点。通过结合实际工程需要和最新研究动态,对这一领域存在的问题和后续发展趋势进行总结。研究对推动声子晶体和声学超材料在工程实践中的应用具有一定的引导意义。

基于散射单元的声子晶体振动带隙研究

硬质芯体及其包覆层构成的复合结构称为散射单元 ,散射单元按照特定的排列方式可以构成声子晶体。文章采用有限元方法分别计算了立方散射单元构成的一维声子晶体及简单立方结构三维声子晶体的振动特性 ,结果表明 ,两种声子晶体的振动带隙有较好的一致性 ,因此 ,对三维声子晶体振动带隙的研究可以简化为对一维声子晶体振动带隙的研究。叠加层数、芯体材料对一维声子晶体振动带隙的影响在文中进行了讨论。最后 ,声子晶体的振动特性测试结果验证了文中的结论。

周期弹簧振子结构振动带隙及隔振特性研究

无限周期弹簧振子结构具有和声子晶体类似的振动(弹性波)带隙,带隙频率范围内的振动(弹性波)在该结构 中无法进行传播。在计算无限周期弹簧振子结构振动(弹性波)带隙的基础上,采用数值方法计算并讨论了有限周 期弹簧振子结构的振动传输特性及隔振特性,最后以双质量周期弹簧振子结构为例,对其振动传输特性及隔振特 性进行了试验验证。

Mg_2Si的声子谱与力热性能的第一性原理计算

针对6xxx系铝合金的主要强化相Mg2Si的力热性能,采用密度泛函理论、第一性原理以及CASTEP软件进行了理论计算,得到了Mg2Si的平衡晶格常数、弹性系数、声子谱、声子态密度以及相关热力学参量,并对计算曲线进行了理论分析.结果表明:合金强化相Mg2Si的刚性较好,脆性较强,在合金中能起到强化作用.通过声子谱及声子态密度曲线可知,存在9条色散关系曲线,其中3条为声学波,6条为光学波,且频率在8.51 THz附近的格波振动较强.随着温度的增加,熵、焓均增加,而自由能减少.当温度低于200 K时,热容量随着温度的增加而明显增加;当温度高于400K后,热容量接近于常量,其计算结果与物理规律一致.

局域共振型磁流变隔振支座低频完全禁带研究

将声子晶体及超材料理论引入磁流变弹性体隔振支座的设计,构建了局域共振型的隔振支座,并研究其低频完全禁带及振幅分布。结果表明,改变共振型超材料单元质量块的形状,系统不仅在低频处出现共振禁带,且在稍高处产生多条布喇格散射宽禁带。这将为隔振支座设计提供新的思路。

二维声子晶体理论在磁流变隔振支座中的应用

基于二维声子晶体模型,设计了周期排列的磁流变隔振支座,采用有限元方法研究其弹性波传输特性和振动能量分布。研究结果表明:隔振支座存在弹性波带隙,通过外加磁场可以调控带隙的带宽和频率位置;缺陷态结构对传输能量有局域作用。

基于声子晶体理论的弹性地基梁的振动特性研究

荷载影响结构的振动特性,引起抗振性能的变化.借助声子晶体理论,研究弹性地基梁的带隙特性,建立了轴向力作用时Winkler地基上声子晶体Euler梁弯曲振动模型,采用改进的传递矩阵法,计算出梁的能带结构,判断出能带结构的变化趋势.研究表明,轴力改变能带结构,带隙范围发生变化.拉力提升带隙,但地基带隙保持不变;压力降低带隙频率,地基带隙随着压力的增加而减小.同时,进行Euler模型的数值模拟,仿真的结果与理论值基本吻合.通过轴力可以调节带隙的频率范围,达到抗振、减振的效果.

声子晶体研究概况

声子晶体是近年来提出的一种新型功能材料,目前主要处于理论研究阶段。通过与光子晶体类比,可推断由振动材料组成的周期性结构,传输弹性波时也有带隙存在,这种特征可以有效地进行声波控制和振动控制,阐述了声子晶体的概念、基本特征、研究方法和进展。

一维声子晶体在防止低频噪声中的应用

应用集中质量法研究了集中质量数n、晶格常数a、组分比t、弹性模量E及密度ρ等因素对一维声子晶体带隙的影响。结果表明,带隙起始频率及带宽随a增加而减小,随t增加而快速增大(当t>1);带隙起始频率随两种材料E差值与ρ差值增加而减小,而带隙截止频率却不变;带隙精度则随n增加而增大。据此设计出一种能屏蔽约59～557Hz范围内低频噪声的复合结构声子晶体。