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     

Low band gap frequencies and multiplexing properties in 1D and 2D mass spring structures

This study reports on the propagation of elastic waves in 1D and 2D mass spring structures.An analytical and computation model is presented for the 1D and 2D mass spring systems with different examples.An enhancement in the band gap values was obtained by modeling the structures to obtain low frequency band gaps at small dimensions.Additionally,the evolution of the band gap as a function of mass value is discussed.Special attention is devoted to the local resonance property in frequency ranges within the gaps in the band structure for the corresponding infinite periodic lattice in the 1D and 2D mass spring system.A linear defect formed of a row of specific masses produces an elastic waveguide that transmits at the narrow pass band frequency.The frequency of the waveguides can be selected by adjusting the mass and stiffness coefficients of the materials constituting the waveguide.Moreover,we pay more attention to analyze the wave multiplexer and DE-multiplexer in the 2D mass spring system.We show that two of these tunable waveguides with alternating materials can be employed to filter and separate specific frequencies from a broad band input signal.The presented simulation data is validated through comparison with the published research,and can be extended in the development of resonators and MEMS verification.     

Complete flexural vibration band gaps in membrane-like lattice structures

The propagation of flexural vibration in the periodical membrane-like lattice structure is studied. The band structure calculated with the plane wave expansion method indicates the existence of complete gaps. The frequency response function of a finite periodic structure is simulated with finite element method. Frequency ranges with vibration attenuation are in good agreement with the gaps found in the band structure. Much larger attenuations are found in the complete gaps comparing to those directional ones. The existence of complete flexural vibration gaps in such a lattice structure provides a new idea for vibration control of thin plates.     

Analysis on band gap properties of periodic structures of bar system using the spectral element method

In this paper, the band gap properties of the periodic structures of bar system, which include the rod-joint, truss, and frame structures, are studied using spectral element method (SEM). The spectral equations of the rod, beam, and joint elements are established and the spectral equations of the whole structures are further assembled. The frequency responses of the whole structures are calculated and the results are compared with those calculated by the finite element method (FEM). It can be observed that the SEM is more accurate in high frequency ranges. The band gap properties of the three types of periodic structures are studied, respectively. Furthermore, the effects of structural length, unit cell number, structural configurations, load conditions, and structural damping on the band gap properties are investigated.     

Line-shape of light absorption by excitons in one-, two- and three-dimensional molecular structures

Within the framework of the dipole approximation the line-shape of light absorption for exciton transitions between narrow bands in one-, two- and three-dimensional periodic structures are calculated. Exciton damping due to lattice imperfections is accounted for as a frequency independent parameter. The obtained analytical expressions allow analysis of the line-shape for different space dimensions of structure depending on bandwidth difference, damping and temperature.     

Light exiting from real photonic band gap crystals is diffuse and strongly directional

Any photonic crystal is in practice periodic with some inevitable fabricational imperfections. We have measured angle-resolved transmission of photons that are multiply scattered by this disorder in strongly photonic crystals. Peculiar non-Lambertian distributions occur as a function of frequency: due to internal diffraction, wide angular ranges of strongly reduced diffuse transmission coincide with photonic stop bands, while enhancements occur for directions outside stop gaps. We quantitatively explain the experiment with a model incorporating diffusion and band structure on equal footing. We predict that in the event of a photonic band gap, diffuse light at frequencies near band gap edges can exit only along isolated directions. Angle-resolved diffuse transmission appears to be the photonic equivalent of angle-resolved photoelectron spectroscopy.     

电磁波在周期介质中的传播及二维光子晶体的光子带结构

光子晶体是光学与凝聚态物理交叉的新领域,也是近年来应用物理学的一个重要研究领域,它是一种由介电常数高的(低的)介质在另一种介电常数低的(高的)背景介质中周期排列所组成的人造多维周期结构材料,能够产生光子带隙。频率落在带隙内的光在晶体里沿任何方向都不能传播,因而具有能够抑制原子、分子的自发辐射等诱人的光电子学特性,在基础研究和实际应用上都有着巨大的潜力。本文在这一领域里进行了富有成效的研究,获得了很好的结果。主要有:(1)利用平面波展开方法来计算二维光子晶体的带隙结构。首先,我们设计正方晶胞的二维光子晶体模型。设x₃方向为介质柱的轴方向,二维周期结构在x₁-x₂平面上。晶胞的晶格常数为a,半径为r,介质柱和空气柱的介电常数分别为ε_a=17和ε_b=1,a>2r。设计的核心思想是通过降低光子晶体结构的对称性,消除光子能带在晶体的布里渊区高对称点上的本征简并。(2)对于二维光子晶体的电磁波理论及周期介质中的Bloch波解做了详细的推导,给出了光子晶体中禁带存在的理论依据。同时以正方格子晶格的二维光子晶体为例,验证了电介质在空气圆孔中的排列存在E偏振和H偏振的光子带隙重叠区,称为绝对光子带隙。对于二维的光子晶体,两种本征偏振模式的光子能带结构可以独立地调节,以实现两者的光子带隙的最优重叠, 从而大大提高了二维光子晶体的完全带隙宽度。     

周期薄壁开口梁中的双耦合振动带隙

本文研究了由两种材料组合构成的周期性薄壁开口梁的弯曲和扭转双耦合振动。基于双耦合振动方程，给出了平面波展开法。当填充比不变时，晶格常数是影响带隙相对宽带的一个因素；当晶格常数和填充比不变时，杨氏模量是影响带隙宽带的主要因素，而不是密度。利用有限元法计算了有限周期结构的振动频率响应，在带隙频率范围内，振动衰减40dB左右。这些发现对于声子晶体的应用具有重要意义。     

Spin waves in periodic magnetic structures—magnonic crystals

Propagation of spin waves (SWs) through a periodic multilayered magnetic structure is analyzed. It is assumed that the structure consists of ferromagnetic layers having the same thickness but different magnetizations. The wave spectrum obtained contains forbidden zones (stop bands) in which wave propagation is prohibited. Introduction into the structure of the ferromagnetic layer with a different thickness breaks the structural symmetry and leads to a localization of the SW mode with the frequency lying in the stop band. Reflection of the wave by the structure of the finite length and transmission of the wave through the structure are also investigated. Numerical calculations of the wave dispersion and the transmission coefficients for symmetrical periodic structures as well as the structures with a defect are presented. Drawing an analogy from photonic crystals known in optics, such magnetic structures can be called one-dimensional (1-D) magnonic crystals (MCs). The possibilities of existence of the 2-D MCs are also discussed.     

Dispersion of light in opal photonic crystal

The selective reflection spectra of films prepared from the photonic crystal, i.e., synthetic opal, are investigated. It is revealed that the refractive index changes at the boundaries of the photonic band gap. The wave vector is renormalized as a result of the interaction of the light wave with the periodic structure of the crystal, and the dependence of the frequency on the photon wave vector deviates from a linear behavior. The band gap determined from these data is approximately equal to 1.7 × 10¹⁴ Hz.     

X形超阻尼局域共振声子晶体梁弯曲振动带隙特性

以声子晶体理论为基础,设计了一种具有超阻尼特性的X形局域共振结构,分析了周期性附加X形局域共振的梁弯曲振动传播特性.利用拉格朗日方程分析了X形局域共振结构动力学等效特性,揭示了该结构的阻尼放大的机理,分析了几何结构参数对于带隙特性的影响,并利用有限元法验证了X形局域共振结构的超阻尼特性.研究结果表明,周期性附加X形局域结构能够有效地抑制低频弯曲振动在梁中的传播,产生超阻尼特性,实现低频、宽带的减振效果,为结构的低频减振提供了一个新的设计方案.     

二维斜三角晶格光子晶体完全带隙研究

在二维正三角晶格光子晶体的基础上,通过改变晶体的晶格基矢构造了一种全新的周期结构。该周期结构的最小周期单元不再是传统意义上的等边三角形,而是一种更为优化的斜三角形结构。利用平面波展开法理论模拟了二维斜三角晶格光子晶体完全带隙的情况,发现所设计结构的完全带隙宽度是二维正三角晶格光子晶体完全带隙宽度的4.3 2倍。分析了介质柱宽度,介质柱旋转角度以及相对介电常数对所构造结构的完全带隙的影响,所得结果对二维光子晶体的理论研究和实际应用有所帮助。为任意角度的二维光子晶体集成波导的研究和制作提供了理论基础。     

高频区具有大带隙的二维像素型光子晶体结构

针对方块像素组成的二维光子晶体，传统平面波展开法可经修正使之收敛速度大大提高。采用快速算法，在高频区域找到了一种具有稳定的较大绝对禁带宽度的GaAs光子晶体结构，绝对禁带宽度为0．0995ωc(ωc-2π／α，α为晶格常量，c为光速)，中心频率为1．2625ω。     

一维指数形变截面有限周期声子晶体的研究

本文利用集中质量法对弹性纵波在一维指数形截面有限周期声子晶体中的传播进行了研究, 得到了频率响应函数的表达式. 与一维等截面的声子晶体相比, 指数形变截面声子晶体带隙内的衰减值随着输出端截面积的增大而减小, 同时带隙的起始频率降低而截止频率升高, 也即带隙的宽度会得到拓展. 晶格常数和材料组份比变化时, 变截面声子晶体带隙的起始频率和截止频率的变化趋势与等截面时的声子晶体相同. 希望本文的研究能够推动声子晶体在减振降噪等领域中的应用.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

Analysis of two-dimensional photonic band gap structure with a rhombus lattice

The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator (HFSS) simulation. General wave vectors in the first Briliouin zone are derived. The relative band gap as a function of air-filling factor and background material is investigated, respectively, and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy. These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.     

Large complete band gap in two-dimensional phononic crystal slabs with elliptic inclusions

Phononic band structure with periodic elliptic inclusions for the square lattice is investigated based on the plane wave expansion method. The numerical results show the systems composed of tungsten (W) elliptic rods embedded in a silicon (Si) matrix can exhibit a larger complete band gap than the conventional circular phononic crystal (PC) slabs. The phononic band structure of the plate-mode waves and the width of the first complete band gap can be tuned by varying the ratio of the minor axis and the major axis, the orientation angle of the elliptic rods and the thickness of the PC slabs. We also study the band structure of plate-mode waves propagating in two-dimensional (2D) slabs with periodic elliptic inclusions coated on uniform substrate.     

Optimal synthesis of 2D phononic crystals for broadband frequency isolation

The spatial distribution of material phases within a periodic composite can be engineered to produce band gaps in its frequency spectrum. Applications for such composite materials include vibration and sound isolation. Previous research focused on utilizing topology optimization techniques to design two-dimensional (2D) periodic materials with a maximized band gap around a particular frequency or between two particular dispersion branches. While sizable band gaps can be realized, the possibility remains that the frequency bandwidth of the load that is to be isolated might exceed the size of the band gap. In this paper, genetic algorithms are used to design squared bi-material unit cells with a maximized sum of band-gap widths, with or without normalization relative to the central frequency of each band gap, over a prescribed total frequency range of interest. The optimized unit cells therefore exhibit broadband frequency isolation characteristics. The effects of the ratios of contrasting material properties are also studied. The designed cells are subsequently used, with varying levels of material damping, to form a finite vibration isolation structure, which is subjected to broadband loading conditions. Excellent isolation properties of the synthesized material are demonstrated for this structure.     

Optimal synthesis of 2D phononic crystals for broadband frequency isolation

The spatial distribution of material phases within a periodic composite can be engineered to produce band gaps in its frequency spectrum. Applications for such composite materials include vibration and sound isolation. Previous research focused on utilizing topology optimization techniques to design two-dimensional (2D) periodic materials with a maximized band gap around a particular frequency or between two particular dispersion branches. While sizable band gaps can be realized, the possibility remains that the frequency bandwidth of the load that is to be isolated might exceed the size of the band gap. In this paper, genetic algorithms are used to design squared bi-material unit cells with a maximized sum of band-gap widths, with or without normalization relative to the central frequency of each band gap, over a prescribed total frequency range of interest. The optimized unit cells therefore exhibit broadband frequency isolation characteristics. The effects of the ratios of contrasting material properties are also studied. The designed cells are subsequently used, with varying levels of material damping, to form a finite vibration isolation structure, which is subjected to broadband loading conditions. Excellent isolation properties of the synthesized material are demonstrated for this structure.     

Effects of Poisson's ratio on the band gaps and defect states in two-dimensional vacuum/solid porous phononic crystals

The effects of the Poisson’s ratio of the solid host on the band gaps and point defect states of the mixed elastic wave modes in two-dimensional vacuum/solid porous PNCs are studied by numerical simulations. Four typical systems are considered. The four systems are, respectively, (I) the system with a square lattice and circular pores, (II) the system with a hexagonal lattice and circular pores, (III) the system with a square lattice and square pores and (IV) the system with a hexagonal lattice and regular-hexagonal pores. In the latter two systems, with respect to the outer boundaries of the Wigner-Seitz unit cell, the pores rotate 45° and 30°, respectively. Some observable effects of the Poisson’s ratio are found in the numerical results. Especially, the variations of the band gap boundaries with the Poisson’s ratio exhibit relatively consistent behaviors. With the increase of the Poisson’s ratio, the normalized frequency of a band gap boundary generally increases, except that in system (III) the normalized frequency of the upper boundary of the first band gap remains almost unchanged. Detailed interpretations on this phenomenon are given.