基于带隙阻波隔振的超材料梁吸隔振一体化设计方法

魏巍; 管峰; 方鑫

doi:10.7498/aps.73.20241135

摘要

先进的振动控制技术在航空航天及船舶领域具有广泛需求. 当前, 大多数系统的吸振与隔振设计分离, 且现有隔振设计难以有效增强低频线谱隔离. 因此, 本文针对典型欧拉梁, 提出了一种吸隔振一体化设计方法. 基于声学超材料的带隙波阻原理, 研究了振动在横向和纵向的传播特性及其协同调节规律. 结果表明, 通过使用波阻隔振器实现多种模态的吸振和隔振, 无需额外结构即可高效控制低频和宽带振动. 在横向通路中, 引入局域共振带隙显著提高了低频隔振效果; 在纵向通路中, 除了近零及Bragg带隙外, 波阻隔振器还能产生多种带隙, 实现了低频宽带吸振. 研究显示, 通过叠加纵向与横向带隙可达成100 Hz内87.3%的带隙占比. 采用有限元法验证了解析结果的准确性. 研究结果为复杂梁、板、管路、框架等结构的吸隔振一体化设计提供了可行思路.

关键词:

超材料 /
带隙 /
吸振 /
隔振

Abstract

Advanced vibration control technology is widely needed in the fields of aerospace and shipbuilding. Currently, separate vibration absorption and isolation design of most systems are separated, and existing isolation designs cannot effectively enhance the isolation of low-frequency line spectra. There is an urgent need to develop integrated vibration absorption and isolation designs and strengthen low-frequency line spectrum control. In response to this need, this paper focuses on a typical Euler beam and the investigation of the propagation characteristics of vibrations in transverse direction and longitudinal direction, the principles of integrated vibration absorption and isolation design, and the synergistic regulation of bandgaps, based on acoustic metamaterial bandgap wave-insulating vibration control configurations and analytical methods. Ultimately, without adding additional structures, the wave-insulating vibration control device is used to generate multiple modes of vibration absorption and isolation simultaneously, achieving an integrated low-frequency, broadband, and high-efficiency vibration absorption and isolation design. This method achieves broadband vibration isolation in the transverse vibration isolation path while also introducing local resonance bandgaps that significantly improve low-frequency vibration isolation. In the longitudinal (forward propagation) path, in addition to near-zero and Bragg bandgaps, multilayer isolators generate multimodal local resonant bandgaps, achieving low-frequency broadband vibration absorption and effective control in the entire frequency range. This paper elucidates the synergistic modulation of longitudinal and transverse bandgaps, showing that by superimposing these bandgaps, an impressive bandgap ratio of 87.3% below 100 Hz across the entire frequency range can be achieved. Furthermore, an entity structure is designed, and the accuracy of the analytical results is verified by using the finite element method. The findings provide feasible design ideas for realizing the integrated vibration absorption and isolation of complex structures such as beams, plates, pipelines, and frames.

Keywords:

作者及机构信息

1.
国防科技大学智能科学学院, 长沙　410073

2.
海军研究院, 北京　100161

通信作者: 方鑫, xinfangdr@sina.com

基金项目: 国家自然科学基金(批准号: 52241103, 52322505)和湖南省自然科学基金(批准号: 2023JJ10055)资助的课题.

Authors and contacts

1.
College of Intelligent Science, National University of Defense Technology, Changsha 410073, China

2.
Naval Research Academy, Beijing 100161, China

Corresponding author: Fang Xin, xinfangdr@sina.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52241103, 52322505) and the Natural Science Foundation of Hunan Province, China (Grant No. 2023JJ10055).

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 传统周期支撑梁的振动传递特性分析　(a) 振动传播路径示意图; (b)不同f₀下的近端支撑的横向振动传递率; (c) 不同f₀下的远端支撑的横向振动传递率; (d)右端截面的纵向振动传递率

Fig. 1. Analysis of vibration propagation in a traditional periodic support structure of a beam: (a) Schematic diagram of the vibration propagation path; (b) transverse vibration transmission ratio of the proximal support at different f₀; (c) transverse vibration transmission ratio of the distal support at different f₀; (d) longitudinal vibration transmission ratio of the right-end section.

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图 2 吸隔振一体超材料梁的结构设计　(a)理论模型; (b)元胞模型

Fig. 2. Structural design of a vibration isolation and absorption integrated metamaterial beam: (a) Theoretical model; (b) metacell model.

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图 3 传统结构和吸隔振一体结构在近端的支撑结构的振动传动率　(a)传递率曲线; (b)传统隔振结构; (c)多层隔振结构; (d)吸隔振一体结构

Fig. 3. Vibration transmission ratio of the traditional structure and the integrated vibration isolation and absorption structure at proximal support structure: (a) Transmission ratio curve; (b) traditional vibration isolation structure; (c) multi-layer vibration isolation structure; (d) integrated vibration isolation and absorption structure.

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图 4 横向波矢虚部和近端支撑结构的传递率曲线　(a)波矢虚部; (b)近端支撑结构的传递率曲线

Fig. 4. Imaginary part of the transverse wave vector and transmission ratio curve of the proximal support structure: (a) Imaginary part of the wave vector; (b) transmission ratio curve of the proximal support structure.

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图 5 不同形式支撑梁的元胞模型和对应纵向衰减系数　(a)多层隔振模型纵向衰减系数; (b)吸隔振一体模型纵向衰减系数; (c) 多层隔振模型示意图; (d) 吸隔振一体模型示意图

Fig. 5. Metacell models and corresponding longitudinal attenuation coefficients of support beams in different configurations: (a) Longitudinal attenuation coefficient of the multi-layer vibration isolation model; (b) longitudinal attenuation coefficient of the integrated vibration isolation and absorption model; (c) schematic diagram of multi-layer vibration isolation model; (d) schematic diagram of integrated vibration isolation and absorption model.

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图 6 吸隔振一体结构的振动传递特性　(a)纵向和横向上的弹性波衰减系数; (b)远端支撑结构的传递率曲线

Fig. 6. Vibration transmission characteristics of the integrated vibration isolation and absorption structure: (a) Longitudinal and transverse attenuation coefficient; (b) transmission ratio curve of the distal support structure.

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图 7 频率比G的调制规律　(a) G对于纵向带隙的调制规律; (b) G对于横向带隙的调制规律; (c) G对于叠加带隙的影响; (d) G对于传递率的影响

Fig. 7. Modulation rules of frequency ratio G: (a) Modulation rules of G for longitudinal bandgaps; (b) modulation rules of G for transverse bandgaps; (c) the effect of G on superimposed band gaps; (d) the effect of G on transmission ratio.

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图 8 质量比r和附加质量比$\beta $的调制规律　(a)横向LR带隙起始频率的调制; (b) $\beta $对于横向LR带隙的宽度影响; (c) r对于横向LR带隙的宽度影响; (d)附加质量比$\beta $的归一化传递率

Fig. 8. Modulation law of the mass ratio r and the additional mass ratio $\beta $: (a) Modulation of the starting frequency of the transverse LR bandgap; (b) the effect of the additional mass ratio $\beta $ on the width of the transverse LR bandgap; (c) the effect of r on the width of the transverse LR bandgap; (d) the normalized transfer rate of the additional mass ratio $\beta $.

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图 9 Bragg带隙与LR带隙的协同调制　(a) 3阶LR带隙与Bragg的协同调制; (b) 3种近似耦合带隙的衰减系数曲线

Fig. 9. Synergistic modulation of Bragg band gaps and LR bandgaps: (a) Collaborative modulation of third-order LR bandgap and Bragg; (b) attenuation coefficient curves of three approximate coupled bandgaps.

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图 10 Bragg带隙与1st LR带隙的协同调制　(a)纵向和横向的衰减系数; (b)近端和远端的传递率曲线

Fig. 10. Synergistic modulation of Bragg bandgaps and 1st LR bandgap: (a) Longitudinal and transverse band structures; (b) transmission ratio curves of proximal and distal supports.

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图 11 损耗因子${\eta _1}$和${\eta _2}$对于衰减系数和传递率曲线的影响　(a) 不同损耗因子${\eta _1}$对应的衰减系数; (b) 不同损耗因子${\eta _1}$对应的传递率曲线; (c) 不同损耗因子${\eta _2}$对应的衰减系数; (d) 不同损耗因子${\eta _2}$对应的传递率曲线

Fig. 11. Effects of attenuation factor ${\eta _1}$ and ${\eta _2}$ on attenuation coefficient and transmission ratio curves: (a) Attenuation coefficient corresponding to different ${\eta _1}$; (b) transmission ratio curves corresponding to different ${\eta _1}$; (c) attenuation coefficient corresponding to different ${\eta _2}$; (d) transmission ratio curves corresponding to different ${\eta _2}$.

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图 12 吸隔振一体超材料梁的示意图　(a) 超材料梁模型; (b)超材料梁的元胞; (c)元胞中波阻隔振器

Fig. 12. Schematic diagram of the vibration isolation and absorption integrated metamaterial beam: (a) Metamaterial beam model; (b) metacell of the metamaterial beam; (c) metacell of the wave-insulating vibration isolator.

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图 13 5周期的吸隔振一体超材料梁的振动特性　(a)谱元法和有限元法计算得到的振动传递率对比; (b)特定频率下的吸隔振一体超材料的振动响应

Fig. 13. Vibration characteristics of the 5-period vibration isolation and absorption integrated metamaterial beam: (a) Comparison of vibration transmission ratios obtained by the spectral element method and the finite element method; (b) vibration response of the integrated vibration isolation and absorption metamaterial at specific frequencies.

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图 14 (a)不同损耗因子下的传递率曲线; (b)与传统单自由度隔振器的传递率对比

Fig. 14. (a) Transmission ratio curves under different attenuation factors; (b) comparison with the transmission ratio of a traditional single-degree-of-freedom isolator.

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表 1 三种耦合方式的带隙宽度和总宽度

Table 1. Bandgap width and total width of the three coupling modes.

晶格常数		a/mm
晶格常数		3000	3850	3360	3220
1st	起始频率/Hz	21.4—26.0	18.2—29.4	19.9—25.2	20.3—25.2
1st	宽度/Hz	4.4	11.2	5.3	4.9
2nd	起始频率/Hz	31.7—33.8	32.6—34.5	30.2—34.7	30.6—32.8
2nd	宽度/Hz	2.1	1.9	4.5	2.2
3rd	起始频率/Hz	35.5—36.1	35.3—36.2	35.4—36.3	34.7—36.3
3rd	宽度/Hz	0.6	0.9	0.9	1.6
4th	起始频率/Hz	36.8—37.0	36.3—40	36.4—43.7	36.4—45.5
4th	宽度/Hz	0.2	4.7	7.3	9.1
总宽度/Hz		7.3	18.7	18.0	17.8

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map

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基于带隙阻波隔振的超材料梁吸隔振一体化设计方法