硅酸盐学报

耦合声学黑洞结构的飞碟型声子晶体宽频带隙机理

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陈俊豪 ¹^,² , 李俣慧 ¹ , 陈国东 ¹ , 龙广成 ² , 谢友均 ² , 曾晓辉 ³

硅酸盐学报 | 研究论文 2025,53(11): 3352-3361

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硅酸盐学报 |研究论文 2025 , 53 (11) : 3352 -3361

耦合声学黑洞结构的飞碟型声子晶体宽频带隙机理

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陈俊豪¹^,², 李俣慧¹, 陈国东¹, 龙广成², 谢友均², 曾晓辉³

作者信息

^1．内江师范学院建筑工程学院，四川内江 641000

^2．中南大学土木工程学院，长沙 410000

^3．海南大学基建处，海口 570100

通讯作者:

曾晓辉（1982—），男，博士，教授。

作者简介:

陈俊豪（1993—），男，博士，讲师。

Broadband Bandgap Mechanism of Flying Saucer Shaped Phononic Crystals Coupled to Acoustic Black Hole Structure

Junhao CHEN¹^,², Yuhui LI¹, Guodong CHEN¹, Guangcheng LONG², Youjun XIE², Xiaohui ZENG³

Affiliations

^1.School of Architectural Engineering, Neijiang Normal University, Neijiang 641000, Sichuan, China

^2.School of Civil Engineering, Central South University, Changsha 410000, China

^3.Infrastructure Department, Hainan University, Haikou 570100, China

Corresponding Author:

ZENG Xiaohui (1982-), male, Ph.D., Professor. E-mail: zxhzlh@126.com

CHEN Junhao (1993-), male, Ph.D., Lecturer. E-mail: 359622670@qq.com

出版时间: 2025-11-20 doi: 10.14062/j.issn.0454-5648.20250036

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摘要

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为实现宽频带隙的声子晶体设计，本工作将仿生设计与声学黑洞结构相结合，基于局域共振理论，提出了一种飞碟型声子晶体。通过有限元法对该声子晶体的能带结构、振动模式及衰减特性进行计算，揭示了其带隙产生机理，并分析了几何参数对带隙的影响规律。结果表明：飞碟型声子晶体在0~1000 Hz产生了1条局域共振带隙，位于294~944 Hz，带隙宽度为650 Hz，带隙覆盖率为65%。带隙起始频率主要由散射体的平移振动决定，而截止频率则是由边缘结构左右两侧的反向振动决定。增加小梯形的高度可以提高带隙的起始频率，增加矩形的宽度可以调整带隙的截止频率，调整大梯形的高度则可影响带隙宽度。

关键词

带隙 / 声子晶体 / 仿生设计 / 声学黑洞 / 局域共振

Abstract

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Introduction

In the field of vibration and noise reduction, phononic crystals and their ability to regulate elastic wave propagation have attracted significant attention. Leveraging the bandgap characteristics of phononic crystals, researchers can precisely control elastic wave transmission within specific frequency ranges. To this end, numerous scholars have dedicated efforts to designing and optimizing novel phononic crystals while investigating their bandgap formation mechanisms. Biomimetic design, which innovates engineering solutions by emulating forms, structures, and functions from nature or existing systems, has emerged as a vital source of inspiration for developing advanced phononic crystals in recent years. Furthermore, the acoustic black hole (ABH) structure, an engineered design that leverages wave manipulation characteristics to achieve energy focusing and absorption of acoustic waves, has been demonstrated to effectively optimize phononic crystal configurations, thereby significantly enhancing their bandgap properties. Aiming to achieve broad bandgap implementation in phononic crystal design, this study integrates biomimetic concepts with the ABH structures and proposes a flying saucer shaped phononic crystal configuration based on local resonance theory.

Methods

Currently, the bandgaps of phononic crystals are primarily determined through plane wave expansion (PWE), finite-difference time-domain (FDTD), lumped mass methods, and finite element method (FEM). The FEM demonstrates distinct advantages in calculating unit cell bandgaps and has been widely adopted. The fundamental principle of bandgap computation using FEM involves three key stages: First, the unit cell analytical model is discretized into finite elements, where the continuous field within each element is characterized by nodal forces and displacements. Subsequently, finite element equations are established based on equilibrium conditions, incorporating Bloch-Floquet periodic boundary conditions to derive an eigenvalue equation containing wavevector-frequency relationships. Ultimately, solving this eigenvalue equation yields the dispersion relations of the equivalent model. This study employs the COMSOL Multiphysics finite element analysis platform to solve the eigenvalue problem, thereby obtaining the band structure of the phononic crystal while simultaneously acquiring its vibration modes.

Results and discussion

The flying saucer shaped phononic crystal proposed in this study exhibits pronounced bandgap characteristics, generating a local resonance bandgap within the 0-1000 Hz frequency range. Specifically, the bandgap spans from 294 Hz to 944 Hz with a width of 650 Hz, exhibiting a relative coverage ratio of 65% over the target frequency spectrum.

The parametric analysis reveals significant geometric sensitivity of bandgap characteristics: 1) With the rectangular width h₁ increasing from 2 mm to 4 mm, the bandgap starting frequency decreases from 352 Hz to 280 Hz while the cut-off frequency elevates from 845 Hz to 961 Hz, resulting in a 38.1% bandwidth enhancement from 493 Hz to 681 Hz; 2) As the large trapezoidal height a₂ grows from 0.6 mm to 1.4 mm, the bandgap shifts downward from 402-1312 Hz to 248-734 Hz, accompanied by a 46.6% bandwidth reduction from 910 Hz to 486 Hz. 3) When the small trapezoidal height a₃ escalates from 0.3 mm to 1.2 mm, the initial frequency increases by 13.2% (288 Hz to 326 Hz) whereas the cut-off frequency drops by 33.3% (1170 Hz to 780 Hz), collectively causing a 48.5% bandwidth decrease from 882 Hz to 454 Hz.

Conclusions

The bandgap characteristics of the flying saucer shaped phononic crystal are determined by the vibration modes of its constituent structures. Specifically, the bandgap starting frequency is primarily governed by the translational vibration of the resonator, while the cut-off frequency results from the reverse-phase vibrations on both sides of the edge structure.

When the excitation frequency falls within the bandgap range, the flying saucer shaped phononic crystal effectively localizes vibrational energy. Most energy is confined within the internal structure, particularly at the resonator and edge regions, with minimal energy transmitted to the output terminal. This process achieves strong vibration suppression, thereby fulfilling the objectives of vibration reduction and noise control.

The bandgap characteristics of the flying saucer shaped phononic crystal, especially the bandgap position and width, are predominantly influenced by the equivalent mass of the resonator, the equivalent mass of the edge structure, and the equivalent stiffness of the soft coating. Geometric parameter optimization enables precise bandgap tuning: increasing the small trapezoidal height elevates the bandgap starting frequency; enlarging the rectangular width adjusts the cutoff frequency; and modifying the height of the large trapezoid alters the bandgap width.

The flying saucer shaped phononic crystal proposed in this study exhibits bandgap characteristics. By configuring the flying saucer shaped phononic crystal into composite acoustic absorption panels through periodic array arrangements, this design fully exploits its low-frequency local resonance bandgap characteristics spanning 650 Hz, providing innovative solutions for multi-domain vibration and noise control. In automotive engineering, the panels can be embedded within door cavities, roof structures, or chassis interlayers to suppress road-induced tire noise (200-500 Hz) and engine resonance harmonics. For rail transit applications, integrating the panels into carriage wallboards, bogie systems, or track underlayments enables simultaneous attenuation of wheel-rail friction noise (500-800 Hz) and carbody structural vibrations (300-600 Hz). This innovative approach offers a mechanism-driven yet engineering-feasible solution for industrial noise and vibration mitigation, demonstrating significant practical potential.

Key words

bandgap / phononic crystal / bionic design / acoustic black hole / local resonance

引用本文

陈俊豪, 李俣慧, 陈国东, 龙广成, 谢友均, 曾晓辉. 耦合声学黑洞结构的飞碟型声子晶体宽频带隙机理. 硅酸盐学报, 2025 , 53 (11) : 3352 -3361 . DOI: 10.14062/j.issn.0454-5648.20250036

Junhao CHEN, Yuhui LI, Guodong CHEN, Guangcheng LONG, Youjun XIE, Xiaohui ZENG. Broadband Bandgap Mechanism of Flying Saucer Shaped Phononic Crystals Coupled to Acoustic Black Hole Structure[J]. Journal of the Chinese Ceramic Society, 2025 , 53 (11) : 3352 -3361 . DOI: 10.14062/j.issn.0454-5648.20250036

基金

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国家重点研发计划(2023YFB2604300)
国家自然科学基金(52078490)
内江市基础研究与应用基础研究项目(2024NJJCYJN-JSY014)
内江师范学院大学生创新创业训练计划资助项目(X2024009; X2024072)

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2025年第53卷第11期

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文章信息

doi: 10.14062/j.issn.0454-5648.20250036

接收时间：2025-01-15
首发时间：2026-10-21
出版时间：2025-11-20

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出版历史

收稿日期：2025-01-15
修回日期：2025-03-11

基金

国家重点研发计划(2023YFB2604300)

国家自然科学基金(52078490)

内江市基础研究与应用基础研究项目(2024NJJCYJN-JSY014)

内江师范学院大学生创新创业训练计划资助项目(X2024009; X2024072)

作者信息

^1．内江师范学院建筑工程学院，四川内江 641000

^2．中南大学土木工程学院，长沙 410000

^3．海南大学基建处，海口 570100

通讯作者:

曾晓辉（1982—），男，博士，教授。

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20250036

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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