Petrov–Galerkin method for the band structure computation of anisotropic and piezoelectric phononic crystals

Wang, Liqun; Zheng, Hui; Zhao, Meiling; Shi, Liwei; Hou, Songming

doi:10.1016/j.apm.2020.08.026

Cited by 10 publications

(6 citation statements)

References 26 publications

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“…Huang et al [ 113 ] and Lossouarn et al [ 114 ] used the wave FEM to solve the transmission spectrum and energy band of 1D piezoelectric composite beams. Wang et al [ 115 ] calculated the bandgap of 2D piezoelectric PCs with complex-shaped scatterers using the Petrov–Galerkin FEM. Because the FEM requires more grid elements, the calculation amount is large, and the calculation time is long.…”

Section: Calculation Of Bandgapsmentioning

confidence: 99%

Advances in Tunable Bandgaps of Piezoelectric Phononic Crystals

Wang,

Xu,

2023

Materials

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Bandgaps of traditional phononic crystals (PCs) are determined using structural geometric parameters and material properties, and they are difficult to tune in practical applications. Piezoelectric PCs with lead zirconium titanate piezoelectric ceramics (abbreviated to piezoelectric PCs) have multi-physics coupling effects and their bandgaps can be tuned through external circuits to expand the application range of the PCs. First, the typical structures of piezoelectric PCs are summarized and analyzed. According to the structure, common tunable piezoelectric PCs can be roughly divided into three categories: PCs that only contain piezoelectric materials (single piezoelectric PCs), PCs composed of embedded piezoelectric materials in elastic materials (composite piezoelectric PCs), and PCs that are composed of an elastic base structure and attached piezoelectric patches (patch-type piezoelectric PCs). Second, the tuning methods of bandgaps for piezoelectric PCs are summarized and analyzed. Then, the calculation methods of the bandgaps of piezoelectric PCs are reviewed and analyzed. Finally, conclusions are drawn on the research status of piezoelectric PCs, shortcomings of the existing research are discussed, and future development directions are proposed.

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Section: Calculation Of Bandgapsmentioning

confidence: 99%

Advances in Tunable Bandgaps of Piezoelectric Phononic Crystals

Wang,

Xu,

2023

Materials

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“…内嵌式压电/弹性复合材料型压电声子晶体与超材料(下文同样简称为压电/弹性声子晶体或超材料) 指的是将压电材料作为声子晶体/超材料的散射体或基体，根据其周期性可以将其分为一维 [23] 、二维 [6] 和三维体系 [24] ，如图 1(b)所示。 2004 年，Qian 等人 [25] 研究了反平面 SH 波在一维压电/弹性声子晶体中的传播特性，重点分析了周期结构的滤波效应，以及压电/弹性材料的体积比和剪切模量比对相速度的影响。随后，一些研究工作指出通过改变力学、电学界面条件 [26,27] 或施加预应力的方式 [28] 可以调节弹性波在一维压电 /弹性声子晶体中的传播性质。除了这些层状结构，Li 和 Guo [29] 研究了压电/弹性材料组成的杆中纵波的传播特性。对于压电/弹性材料组成的声子晶体杆，Degraeve 等人 [30] 研究了压电/弹性材料组合形成的声子晶体杆内弹性波的传播特性；Parra 等人 [24] 将分流电路接在压电材料两端使得带隙中 Fomenko 等人 [34] 亦对一维叠层压电/弹性声子晶体中界面缺陷对于弹性波传播的影响进行了理论和数值研究。与一维体系相比，二维和三维压电/弹性声子晶体的能带结构较为复杂。Hou 等人 [6] 于 2004 年利用平面波展开法计算得到了压电散射体/聚合物基体的二维压电/弹性声子晶体的能带结构，其研究结果表明当散射体的填充率较大时压电效应才可以显著地提升弹性波带隙的宽度。随后，Wang 等人 [35,36] 针对不同形状散射体和不同晶格形式的二维压电/弹性声子晶体开展了理论研究，详细讨论了声子晶体各个参数对弹性波带隙的影响。Miranda Jr.等人 [37] 利用压电材料作为圆形散射体制成了二维压电声子晶体。Li 等人 [38] 研究了随机失谐(包括散射体的位置和尺寸失谐)对二维压电/弹性声子晶体弹性波带隙的影响。最近，Wang 等人 [39] 利用 Petrov-Galerkin 有限元法计算得到了具有复杂形状散射体的二维压电/弹性声子晶体的能带结构。对于三维压电/弹性声子晶体，Wang 等人 [25] 于 2009 年利用平面波展开法计算得到了三维面心立方压电/弹性声子晶体的能带结构，分别讨论了压电散射体/聚合物基体、以及聚合物散射体/压电基体两种声子晶体形式。其结果显示，将压电球置于聚合物基体内可以产生较宽的弹性波带隙，而且带隙的位置和宽度可以通过材料的压电性质进行调节。随后，他们研究了具有预应力的三维压电 /弹性声子晶体的能带结构，并指出弹性波带隙的上下边界可以通过施加不同的预应力进行调节 [40] 。复合压电声子晶体或超材料 [7] ，如图 1(c)和 4(a)所示。相较于前面介绍的单一压电、内嵌压电材料的声子晶体/超材料，这种压电复合机构的分析更为复杂，需要同时考虑压电或力电耦合效应以及外接电路对于弹性波的影响。为了提高分析和计算效率，学者们提出了一些简化的模型用来理论或数值计算弹性波的传播特性。其中最常用的是由 Hagood 和 Flotow [45] 基于压电片内应变和电极上的…”

Section: 内嵌式压电/弹性复合材料型压电声子晶体与超材料unclassified

Smart piezoelectric phononic crystals and metamaterials:State-of-the-art review and outlook

Li¹,

Wang²,

Ma³

et al. 2022

Chin. Sci. Bull.

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As artificially designed novel periodic materials and structures, phononic crystals (PCs) and acoustic/ elastic metamaterials (AMs) have many unique and extraordinary wave propagation characteristics, which provide a novel research pathway and a promising application opportunity for the efficient vibration control and precise elastic wave manipulation. However, the conventional PCs/AMs after their design and fabrication can be hardly modified with respect to their geometrical and material parameters in order to meet the actual demands, which significantly restricts their practical applications. Smart piezoelectric PCs/AMs based on the piezoelectric or electro-mechanical coupling effect can be utilized to manipulate their vibration or elastic wave propagation properties on demand by controlling the electrical field. This feature can significantly broaden the practical application ranges of the conventional PCs/AMs. This paper first classifies the smart piezoelectric PCs/AMs according to the different combination forms of the piezoelectric and elastic materials or structures roughly into three types. The first type is the unitary or monotype piezoelectric PCs/AMs, which only contain a single piezoelectric material without or with electrodes. The second type is the embedded or infill piezoelectric PCs/AMs in which the piezoelectric scatterers are embedded into an elastic matrix or vice versa. The third type is the externally bonded piezoelectric composite PCs/AMs which consist of the piezoelectric patches attached to the surfaces of an elastic base structure (rod, beam, plate, etc.). Then, based on this classification and according to the dimensional periodicity as well as the tuning method and the tuning target, the state-of-the-art research topics on the different smart piezoelectric PCs/AMs and their potential applications are briefly reviewed.

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“…Veres 11 developed a novel method to study the complex EB structure of square, cross, and other scatterer PnCs based on the FEM, whereas this method is only limited to solid vacuum PnCs. Wang 12 examined the EB structure of scatterer PnCs with different shapes (e.g., triangle, ring, and circle) using the Petrov Galerkin method and verified the effectiveness of this method. However, they did not consider the effect of a rotation angle on scatterers of different shapes.…”

Section: Introductionmentioning

confidence: 97%

Band Gap and Waveguide Characteristics of Petal-Shaped Scatterer Phononic Crystals

Li¹,

Xiang²,

Wang³

et al. 2023

The International Journal of Acoustics and Vibration

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In this study, the Bragg petal-shaped scatterer (PS) phononic crystal (PnC) model is built to expand the width of band gap (BG). The BG characteristics of the PSPnC, square, circular, octagonal, and the "+" shaped scatterer PnC are compared using the finite element method (FEM). This study investigates the effects of the internal and external diameter ratio and the number of petals of single-layer petals, double-layer petals and the application of pre-deformation without changing their structure on the BG characteristics of PnCs for the transmission characteristics of supercell structures. Moreover, two different waveguides (WGs) are built with pre-deformed unit cells as the defects. As revealed by the results, the PSPnC exhibited better vibration isolation performance than PnCs with other shapes. More BGs will appear at a higher frequency with the decrease in the ratio of inner and outer diameter of petals and the increase in the number of petals. In addition, the double-layer PSPnC has high performance, and the dislocation arrangement of PS can enhance the vibration isolation performance of PSPnC. Furthermore, the WG structure is capable of guiding the energy, which provides a new insight into the establishment of the filter.

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Petrov–Galerkin method for the band structure computation of anisotropic and piezoelectric phononic crystals

Cited by 10 publications

References 26 publications

Advances in Tunable Bandgaps of Piezoelectric Phononic Crystals

Advances in Tunable Bandgaps of Piezoelectric Phononic Crystals

Smart piezoelectric phononic crystals and metamaterials:State-of-the-art review and outlook

Band Gap and Waveguide Characteristics of Petal-Shaped Scatterer Phononic Crystals

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