Methods for Broadening the Band Gap Width of Local Resonance Elastic Metamaterial Beams

WANG Gang; WAN Shaoke; HONG Jun; LI Lele; LIU Shuo; LI Xiaohu

doi:10.7652/xjtuxb202410006

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Methods for Broadening the Band Gap Width of Local Resonance Elastic Metamaterial Beams

更新时间：2025-07-28

- Methods for Broadening the Band Gap Width of Local Resonance Elastic Metamaterial Beams
- Vol. 58, Issue 10, Pages: 63-71(2024)
- 作者机构：
  
  1. 西安交通大学现代设计及转子轴承系统教育部重点实验室,西安,710049
  2. 西安交通大学机械工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202410006
  CLC： TB535
- Online First：10 October 2024，
  
  Published：2024
- 稿件说明：
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WANG Gang, WAN Shaoke, HONG Jun, et al. Methods for Broadening the Band Gap Width of Local Resonance Elastic Metamaterial Beams[J]. 2024, 58(10): 63-71.
DOI：

WANG Gang, WAN Shaoke, HONG Jun, et al. Methods for Broadening the Band Gap Width of Local Resonance Elastic Metamaterial Beams[J]. 2024, 58(10): 63-71. DOI： 10.7652/xjtuxb202410006.

摘要

针对传统局域共振弹性超材料存在禁带宽度窄的问题

引入非均匀分布振子设计方法

在不改变振子总质量的前提下实现了禁带拓宽。首先

采用谱元法(SEM)建立通用弹性超材料梁模型

对单、双层均匀振子超材料梁结构的振动传递特性进行分析; 然后

保持振子总质量相等

提出单、双层非均匀振子超材料梁的设计策略; 最后

搭建实验装置对所提结构的振动抑制性能进行测试。研究结果表明:振子间的特征频率差异越大

最终形成的禁带宽度越宽

但禁带范围内的频响曲线会大幅波动

此时可通过加入适当阻尼进行抑制

使禁带曲线变得平稳; 对于双振子超材料梁

振子的质量比和阻尼均会对结构的禁带特性产生影响

在振子与梁质量相同的条件下

单层非均匀及均匀振子超材料梁可分别形成带宽为440、68 Hz的禁带

双层非均匀及均匀振子超材料梁可分别形成带宽为395、40 Hz的禁带。研究表明所提超材料结构能够有效实现振动抑制

可为周期结构的振动问题提供一种新的调控方法。

Abstract

To address the issue of narrow band gap width in traditional local resonance elastic metamaterials

a design approach is introduced that employs non-uniformly distributed resonators to widen the band gap without modifying the total mass of the resonators. Firstly

a generalized elastic metamaterial beam model is established using the spectral element method(SEM)

and the vibration transmission characteristics of both single-and double-layer metamaterial beams with uniform resonators are analyzed. Subsequently

a design strategy for single-and double-layer metamaterial beams with non-uniform resonators is proposed while maintaining a constant total mass of the resonators. Finally

an experimental setup is devised to evaluate the vibration suppression performance of the proposed structures. The findings indicate that a wider band gap is achieved when there is a greater difference in eigenfrequencies between the resonators. However

the frequency response curve within the band gap range may exhibit significant fluctuations

which can be mitigated by introducing appropriate damping to stabilize the band gap curve. The band gap properties of the structure in double-layer metamaterial beams are influenced by both the mass ratio and damping of the resonators. Under the condition of equal mass between the resonators and the beam

the single-layer metamaterial beam with non-uniform and uniform resonators exhibits band gaps with widths of 440 Hz and 68 Hz

respectively. Similarly

the double-layer metamaterial beam with non-uniform and uniform resonators displays band gaps with widths of 395 Hz and 40 Hz

respectively. The study demonstrates that the proposed metamaterial structures effectively achieve vibration suppression

providing a novel approach to address vibration-related challenges in periodic structures.

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references

温卓群, 王鹏飞, 张雁, 等. 面向大尺度结构的力学超材料减振技术 [J]. 航空学报, 2018, 39(S1): 150-154.

WEN Zhuoqun, WANG Pengfei, ZHANG Yan, et al. Vibration reduction technology of mechanical metamaterials presented to large scale structures [J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(S1): 150-154.

吴九汇, 马富银, 张思文, 等. 声学超材料在低频减振降噪中的应用评述 [J]. 机械工程学报, 2016, 52(13): 68-78.

WU Jiuhui, MA Fuyin, ZHANG Siwen, et al. Application of acoustic metamaterials in low-frequency vibration and noise reduction [J]. Journal of Mechanical Engineering, 2016, 52(13): 68-78.

PAI P F, PENG Hao, JIANG Shuyi. Acoustic metamaterial beams based on multi-frequency vibration absorbers [J]. International Journal of Mechanical Sciences, 2014, 79: 195-205.

LIU Zhengyou, ZHANG Xixiang, MAO Yiwei, et al. Locally resonant sonic materials [J]. Science, 2000, 289(5485): 1734-1736.

LI Zhengwei, WANG Xiaodong. Wave propagation in a dual-periodic elastic metamaterial with multiple resonators [J]. Applied Acoustics, 2021, 172: 107582.

LU Kuan, TIAN Yongjun, GAO Nansha, et al. Propagation of longitudinal waves in the broadband hybrid mechanism gradient elastic metamaterials rods [J]. Applied Acoustics, 2021, 171: 107571.

LIN Siqi, ZHANG Yongshan, LIANG Yingjing, et al. Bandgap characteristics and wave attenuation of metamaterials based on negative-stiffness dynamic vibration absorbers [J]. Journal of Sound and Vibration, 2021, 502: 116088.

LIU Panxue, ZUO Shuguang, WU Xudong, et al. Study on the vibration attenuation property of one finite and hybrid piezoelectric phononic crystal beam [J]. European Journal of Mechanics: A Solids, 2020, 84: 104017.

THOMES R L, MOSQUERA-SÁNCHEZ J A, DE MARQUI C. Bandgap widening by optimized disorder in one-dimensional locally resonant piezoelectric metamaterials [J]. Journal of Sound and Vibration, 2021, 512: 116369.

李锁斌, 魏儒义, 周安安, 等. 超结构夹芯板及其低宽频振动带隙机理 [J]. 西安交通大学学报, 2021, 55(4): 77-85.

LI Suobin, WEI Ruyi, ZHOU An'an, et al. A new sandwich type metamaterial plate and its mechanism of low-frequency broad vibration band gap [J]. Journal of Xi'an Jiaotong University, 2021, 55(4): 77-85.

李丽霞, 杨继博, 吕锐翔, 等. 新型环状谐振径向弹性超材料结构低频带隙机理研究 [J]. 西安交通大学学报, 2020, 54(11): 91-97.

LI Lixia, YANG Jibo, LÜ Ruixiang, et al. Low-frequency band gap mechanism of radial elastic metamaterial with new ring resonance [J]. Journal of Xi'an Jiaotong University, 2020, 54(11): 91-97.

YU Dianlong, LIU Yaozong, ZHAO Honggang, et al. Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom [J]. Physical Review: B, 2006, 73(6): 064301.

李锁斌, 陈天宁, 奚延辉, 等. 声子晶体板中低频完全禁带形成机理研究 [J]. 西安交通大学学报, 2016, 50(12): 51-57.

LI Suobin, CHEN Tianning, XI Yanhui, et al. Forming mechanisms of low-frequency complete band gaps in phononic crystal plate [J]. Journal of Xi'an Jiaotong University, 2016, 50(12): 51-57.

李锁斌, 窦益华, 陈天宁, 等. 局域共振型周期结构振动带隙形成机理 [J]. 西安交通大学学报, 2019, 53(6): 169-175.

LI Suobin, DOU Yihua, CHEN Tianning, et al. Formation mechanisms of vibration band gaps in locally resonant periodic structures [J]. Journal of Xi'an Jiaotong University, 2019, 53(6): 169-175.

ZHANG Zhen, LI Tuanjie, WANG Zuowei, et al. Band gap characteristics of flexural wave of two-dimensional periodic frame structure composed of locally resonant composite beam [J]. Mechanical Systems and Signal Processing, 2019, 131: 364-380.

罗金雨, 姚凌云, 江国期, 等. 一种圆柱壳类声子晶体振动带隙及振动特性研究 [J]. 振动与冲击, 2019, 38(8): 133-138.

LUO Jinyu, YAO Lingyun, JIANG Guoqi, et al. A study on the vibration band gap and vibration characteristics of a cylindrical shell phononic crystal [J]. Journal of Vibration and Shock, 2019, 38(8): 133-138.

ZUO Shuguang, NI Tianxin, WU Xudong, et al. Studies of band gaps in flexural vibrations of a locally resonant beam with novel multi-oscillator configuration [J]. Journal of Vibration and Control, 2017, 23(10): 1663-1674.

EL-BORGI S, FERNANDES R, RAJENDRAN P, et al. Multiple bandgap formation in a locally resonant linear metamaterial beam: theory and experiments [J]. Journal of Sound and Vibration, 2020, 488: 115647.[19] HU Guobiao, AUSTIN A C M, SOROKIN V, et al. Metamaterial beam with graded local resonators for broadband vibration suppression [J]. Mechanical Systems and Signal Processing, 2021, 146: 106982.

吴志静, 李凤明, 王毅泽. 谱元法研究桁架结构的振动带隙特性 [J]. 计算力学学报, 2013, 30(S1): 92-95.

WU Zhijing, LI Fengming, WANG Yize. Study on truss periodic structures with vibration band gap properties using the spectral element method [J]. Chinese Journal of Computational Mechanics, 2013, 30(S1): 92-95.

WU Zhijing, LIU Wenyu, LI Fengming, et al. Band-gap property of a novel elastic metamaterial beam with X-shaped local resonators [J]. Mechanical Systems and Signal Processing, 2019, 134: 106357.

AN Xiyue, FAN Hualin, ZHANG Chuanzeng. Elastic wave and vibration bandgaps in planar square metamaterial-based lattice structures [J]. Journal of Sound and Vibration, 2020, 475: 115292.

吴志静. 周期结构的振动行为与隔振性能研究 [D]. 哈尔滨: 哈尔滨工业大学, 2015.

SUGINO C, LEADENHAM S, RUZZENE M, et al. On the mechanism of bandgap formation in locally resonant finite elastic metamaterials [J]. Journal of Applied Physics, 2016, 120(13): 134501.

PENG Hao, FRANK PAI P, DENG Haoguang. Acoustic multi-stopband metamaterial plates design for broadband elastic wave absorption and vibration suppression [J]. International Journal of Mechanical Sciences, 2015, 103: 104-114.

王成林, 张之敬, 马斌, 等. 新型阻尼橡胶圈的动态特性测试 [J]. 材料导报, 2006, 20(S1): 273-274.

WANG Chenglin, ZHANG Zhijing, MA Bin, et al. Dynamic characteristic test of the new damping rubber ring [J]. Materials Review, 2006, 20(S1): 273-274.

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