Width Of Complete Band Gap Research Articles

Wide range of wave attenuation in beam-supported stepped hybrid phononic crystals

A beam-supported stepped hybrid phononic crystals (PnCs) was proposed for the wave attenuations in the wide frequency range from 9.4 Hz to 8.4 kHz. For a ternary beam-supported stepped hybrid PnCs composed of three materials, the first complete band gap width is increased by 2.4 times in comparison with the traditional tapered PnCs by the changes of the interfaces of connections. The equivalent spring mass/pendulum model shows the influence of the connecting beam interface size and column cavity height on the band gap. By changing the depth of the tapered column neck embedded in the silicone rubber cladding on the interfaces of connections, the flat band can be eliminated. For a binary beam-supported stepped hybrid PnCs composed of two materials, the width of the first complete band gap can be greatly increased by the changes of the beam characters for connection and the material types. The wave attenuations in the proposed beam-supported stepped hybrid PnCs show that the design of the connection is the most important factor determining the wide frequency range of band gap characteristics. The prototyping samples of the designed PnCs were fabricated by stereo lithography apparatus (SLA) additive manufacturing technology with ZR850 photosensitive resin. The further comparison of the band gap characteristics of the additive manufactured PnCs validates the key role of connections.

Optimization study of bandgaps properties for two-dimensional chiral phononic crystals base on lightweight design

The bandgap properties of phononic crystals are of great influence on the vibration and noise reduction performance for acoustic metamaterial structure. By analyzing the effects of material properties and geometric parameters on the complete bandgap width for phononic crystals, the maximizing the bandgap width problem is discussed. To achieve the goal of increasing the complete bandgap width, the bandgap optimization for chiral phononic crystals is investigated. The hexachiral phononic crystal for example, the material properties (density, wave velocity) and geometric parameters (scatterer diameter, ligaments or coating thickness) are defined as design variables, the bandgap optimization function which considering of mass factors is established. The multi-objective optimization problem is converted into a single objective optimization problem by normalizing the bandgap frequency coefficient. The bandgaps optimization is implemented, the first bandgap width is significantly increased and lower bound is decreased. Finally, the acoustic transmission analysis is conducted to verify the effectiveness of the proposed method. The results in present work provide more understanding the design and application of innovative acoustic metamaterial.

The Calculation of the Band Structure in 3D Phononic Crystal with Hexagonal Lattice

Abstract In this article, the propagation of acoustic waves in the phononic crystals (PCs) of three dimensions with the hexagonal (HEX) lattice is studied theoretically. The PCs are constituted of nickel (Ni) spheres embedded in epoxy. The calculations of the band structure and the density of states are performed using the plane wave expansion (PWE) method in the irreducible part of the Brillouin zone (BZ). In this study, we analyse the dependence of the band structures inside (the complete band gap width) on c/a and filling fraction in the irreducible part of the first BZ. Also, we have analysed the band structure of the ALHA and MLHKM planes. The results show that the maximum width of absolute elastic band gap (AEBG) (0.045) in the irreducible part of the BZ of HEX lattice is formed for c/a=6 and filling fraction equal to 0.01. In addition, the maximum of the first and second AEBG widths are 0.0884 and 0.0474, respectively, in the MLHKM plane, and the maximum of the first and second AEBG widths are 0.0851 and 0.0431, respectively, in the ALHA plane.

Lamb wave band gaps in one-dimensional radial phononic crystal slabs

In this paper, we theoretically investigate the band structures of Lamb wave in one-dimensional radial phononic crystal (PC) slabs composed of a series of alternating strips of epoxy and aluminum. The dispersion relations, the power transmission spectra and the displacement fields of the eigenmodes are calculated by using the finite element method based on two-dimensional axial symmetry models in cylindrical coordinates. The axial symmetry model is validated by three-dimensional finite element model in Cartesian coordinates. Numerical results show that the proposed radial PC slabs can yield several complete band gaps with a variable bandwidth exist for elastic waves. Furthermore, the effects of the filling fraction and the slab thickness on the band gaps are further explored numerically. It is worth observing that, with the increase of the filling fraction, both the lower and upper edges of the band gaps are simultaneously shifted to higher frequency, which results from the enhancement interaction between the rigid resonance of the scatterer and the matrix. The slab thickness is the key parameter for the existence and the width of complete band gaps in the radial PC slabs. These properties of Lamb waves in the radial PC plates can potentially be applied to optimize band gaps, generate filters and design acoustic devices in the rotary machines and structures.

二维介质柱型Archimedes(4，82)复式晶格光子晶体禁带特性研究

采用平面波展开法分别模拟了空气背景下由介质圆柱和方柱构造的二维Archimedes（4，8^2）复式晶格光子晶体的能带结构，讨论了介质柱形状、折射率、填充比和旋转对称性等因素对完全光子禁带的影响．研究发现，当折射率在2．60到5．40之间时，介质圆柱和方柱构造的二维Archimedes（4，8^2）复式晶格光子晶体都出现了完全光子禁带．随着折射率的增大，最大完全禁带宽度并非随之增大而是存在峰值，介质圆柱型晶格在折射率为2．80时出现峰值；介质方柱型晶格在折射率为2．80和4．40两处出现峰值，且旋转介质方柱能够明显增大禁带宽度，同时存在最佳旋转角度．分析结果表明，在最大完全禁带处，折射率、填充比以及旋转角度等因素的变化对禁带特性的影响很小．

Topology design and optimization of nonlinear periodic materials

This paper explores optimal topologies yielding large band gap shifts in one- and two-dimensional nonlinear periodic materials. The presence of a nonlinearity in a periodic material system results in amplitude-dependent dispersion behavior, leading to novel wave-based devices such as tunable filters, resonators, and waveguides. The performance of these devices over a broad frequency range requires large, tunable band gaps, motivating the present study. Consideration of a one-dimensional bilayer system composed of alternating linear and nonlinear layers shows that optimal designs consist of thin, compliant nonlinear layers. This is at first surprising considering the source of the shift originates from only the nonlinear layer; however, thin layers lead to localized stresses that activate the nonlinear character of the system. This trend persists in two-dimensional materials where optimization studies are performed on plane-stress models discretized using bilinear Lagrange elements. A fast algorithm is introduced for computing the dispersion shifts, enabling efficient parametric analyses of two-dimensional inclusion systems. Analogous to the one-dimensional system, it is shown that thin ligaments of nonlinear material lead to large dispersion shifts and group velocity variations. Optimal topologies of the two-dimensional system are also explored using genetic algorithms aimed at producing large increases in complete band gap width and shift, or group velocity variation, without presupposing the topology. The optimal topologies that result resemble the two-dimensional inclusion systems, but with small corner features that tend to enhance the production of dispersion shift further. Finally, the study concludes with a discussion on Bloch wave modes and their important role in the production of amplitude-dependent dispersion behavior. The results of the study provide insight and guidance on selecting topologies and materials which can yield large amplitude-dependent band gap shifts and group velocity variations, thus enabling sensitive nonlinear devices.

Effects of structure parameters on the bandgap of two dimensional Archimedes A7 photonic crystals

PDF HTML阅读 XML下载 导出引用 引用提醒 结构参数对二维Archimedes A7晶格光子晶体禁带的影响 DOI: 作者: 作者单位: 太原理工大学 物理与光电工程学院,太原理工大学 物理与光电工程学院,太原理工大学 物理与光电工程学院,太原理工大学 材料科学与工程学院,太原理工大学 物理与光电工程学院 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金资助项目（项目编号：60927007）与山西省自然科学基金资助项目（项目编号：2011011003-1）资助课题. Effect of structure parameters on the bandgap of two dimensional Archimedes A7 photonic crystals Author: Affiliation: College of Physics and Optoelectronics, Taiyuan University of Technology,College of Physics and Optoelectronics,Taiyuan University of Technology,College of Physics and Optoelectronics, Taiyuan University of Technology,College of Materials Science and Engineering, Taiyuan University of Technology,College of Physics and Optoelectronics, Taiyuan University of Technology Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:利用平面波展开法研究了空气背景中介质圆柱和方柱构造的二维Archimedes A7晶格光子晶体的禁带结构随介质折射率、填充比的变化关系进行了研究,并进一步计算了介质方柱的旋转角度对完全光子禁带宽度的影响。研究发现,介质圆柱构造的Archimedes A7晶格结构在介质柱折射率最低为n=2.40时就出现完全光子禁带，当n=2.60时禁带宽度达到最大值。介质方柱构造的Archimedes A7晶格结构在介质柱折射率n=3.80时完全禁带宽度达到最大值，且随着折射率的增加禁带宽度变化很小；在介质方柱折射率恒定情况下，其最大禁带宽度与旋转角度无关，但旋转后出现完全禁带的填充比范围明显扩大。 Abstract:Plane wave expansion method is introduced to simulate the band structures of two-dimensional photonic crystals made of Archimedes A7 lattice of circular and square dielectric rod in air. The bandgaps of Archimedes A7 lattice with dielectric rods is also discussed as the refractive index, filling fraction and rotation angle change. The results show that the complete bandgap can be obtained when the refractive index is greater than 2.40, the width of complete bandgap reaches the maximum when the dielectric refractive index of the circular rod is equal to 2.60. For the Archimedes A7 lattice of square dielectric rod, the complete bandgap reaches the maximum when the dielectric refractive index equals 3.80.The maximum complete bandgap changes in a narrow range as the refractive index increases. When the rotation angle of the square dielectric rods changes, the maximum bandgaps keeps constant for a fixed refractive index.However after the change of rotation angle, the complete bandgap appears in alarge scale of the filling fraction. 参考文献 相似文献 引证文献

二维光子晶体的完全带隙

Photonics crystal(PhC)is the material in which the refractive index changes periodically and the PhC has a band structure and location mode,this structure can control light.In order to study two-dimensional PhC complete band gap,in this paper,plane wave expansion method was employed to simulate four types of two-dimensional PhC.We study the relationship between the complete bandgap and the variation of column radius r with a fixed lattice constant.We found that hexagonal lattice PhC air holes complete band gap appears in the r=0.42～0.50 μm range,complete band gap width does not increase with the air column radiu r,but there is a maximum width.The maximum band gap width is Δω1=0.08(ωa/2πc).When air column radiu r=0.47～0.50 μm,square lattice PhC exists complete bandgap,the band gap width Δω2=0.02(ωa/2πc).And complete band gap center frequency increases with r.Results indicate that for hexagonal and square GaAs columnar PhC there is no complete band gap.

Effects of orientation and shape of holes on the band gaps in water waves over periodically drilled bottoms

The complete band gaps (CBGs) of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.

Acoustic wave band gaps in triangular and honeycomb two-dimensional phononic crystals

The ultrasonic band gap properties of phononic crystals composed of arrays of steel cylinders immersed in water and arranged according to square, triangular or honeycomb lattices are compared theoretically and experimentally. In all three cases, complete band gaps are obtained, and the conditions of existence are identified by observing the complete band gap width as a function of the size of the inclusions. However, the measured transmission spectra reveal in the hexagonal symmetry cases (triangular and honeycomb lattices) the existence of deaf bands that cause strong attenuation in the transmission, with no band gap being involved. Band gaps and deaf bands are identified by comparing band structure computations for the infinite phononic crystal, obtained by a periodic-boundary finite element method (FEM), with transmission simulations for the finite phononic crystal, obtained using the finite difference time domain (FDTD) method. The possibility of managing phononic wave guides within a defect line channel inside an otherwise perfect triangular lattice phononic crystal is further demonstrated experimentally.

Propagation of Lamb Waves in Phononic-Crystal Plates

AbstractIn this paper, the band structures of Lamb waves in the two-dimensional phononic-crystal plates are calculated and analyzed based on the plane wave expansion method. The phononic-crystal plates are composed of an array of circular crystalline iron cylinders embedded in the epoxy matrix. Square lattice and triangular lattice are analyzed and discussed, respectively. For the square lattice, two complete band gaps exist, and a narrow pass band between the complete band gaps separates them apart. For the triangular lattice, a wide complete band gap existing with the ratio of gap width to midgap frequency Δω/ωm equal to 72% is found. Furthermore, the influence of the plate thickness is crucial for band structures of Lamb waves. Tuning plate thickness can shift the pass bands effectively, and band shifting causes the variation of the width of complete band gap and its opening and closure.