LOW-FREQUENCY VIBRATION ISOLATION AND ENERGY HARVESTING SIMULTANEOUSLY IMPLEMENTED BY A METAMATERIAL WITH LOCAL RESONANCE
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摘要: 振动隔离和能量采集一体化是一种能够将有害振动隔离并转化为电能收集利用的动力学机制. 本文从局域共振超材料存在低频带隙特性出发, 研究了振动隔离和能量采集双功能超材料的动力学行为. 通过在球型磁腔内放置固接了感应线圈的球摆构成具有能量采集功能的球摆型谐振器, 并将其周期性的放置在基体梁中, 可以将带隙频率范围内的振动聚集在谐振器内, 以实现振动隔离和能量采集双功能. 建立了横向激励下双功能超材料梁的动力学方程, 应用Bloch's定理得到超材料的能带结构, 通过有限元仿真验证了理论模型和研究方法. 研究了不同参数下超材料梁的带隙特性. 进一步将一维拓展到二维, 研究了二维双功能超材料板的振动隔离和能量采集性能. 最后, 设计并建造了振动隔离和能量采集一体化双功能超材料动力学实验平台, 解析、数值和实验结果表明, 在局域共振带隙的频率范围内, 超材料梁主体的振动明显被抑制, 与此同时, 振动被局限在谐振器中, 使采集到的电压达到了最大值. 通过对附加谐振器和没有附加谐振器的能带结构和幅频响应的对比, 发现球摆型谐振器的加入可以在低频范围内形成了一个局域共振带隙, 有效提高了超材料梁在低频处的振动隔离和能量采集性能.Abstract: Integration of vibration isolation and energy harvesting is a dynamic mechanism, in which the harmful vibration could be isolated and converted into electrical energy. In this paper, the dynamic behavior of dual-functional metamaterials for vibration isolation and energy harvesting is studied based on the low frequency band gap characteristics of local resonance metamaterials. A spherical pendulum resonator with energy harvesting function is placed in the spherical cavity by fixing the pendulum of the induction coil. The vibration in the range of band gap frequency can be harvested in the resonator, with the aiming at the dual-functions of vibration isolation and energy harvesting. The dynamic equation of dual-functional metamaterial beam under transverse excitation is established, the energy band structure of metamaterial is obtained by using Bloch’s theorem, and the band gap characteristics of metamaterial beam under different parameters are studied. The theoretical model and research method are verified by finite element simulation. Furthermore, the vibration isolation and energy harvesting characteristics of dual-function metamaterial plates are studied. Finally, a dual-functional metamaterial dynamic experimental platform for vibration isolation and energy harvesting is designed and constructed. The analytical, numerical and experimental results demonstrate that the vibration of the metamaterial beam matrix is significantly suppressed in the frequency range of the local resonant band gap. Simultaneously, the vibration is sinked in the resonator, so that the harvested voltage reaches the maximum. The comparison of the energy band structure and amplitude frequency response between with and without the additional resonator reveals that the addition of the spherical pendulum resonator can generate a local resonant band gap in the low frequency range, which can effectively improve the vibration isolation and energy harvesting performance of the metamaterial beam at the low frequency.
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图 1 (a) 双功能超材料模型图; (b)带能量采集功能谐振器模型图
Figure 1. (a) View of the dual-functional metamaterial; (b) a spherical pendulum energy harvester
图 6 超材料梁的能带结构与幅频响应对比(续)
Figure 6. Band-gaps and amplitude-frequency response of metamaterial (continued)
图 10 横向激励下超材料梁的扫频曲线
Figure 10. Sweep curve of metamaterial beam under transverse excitation
图 12 5 × 5超材料板有限元模型示意图和超材料单胞简约Brillouin区间
Figure 12. Finite element model of metamaterial plate and Brillouin zone of metamaterial plate (5 × 5)
图 14 激励点附近谐振器的输出电压曲线
Figure 14. Output voltage curve of resonator near excitation point
表 1 双功能超材料物理参数
Table 1. Parameters of a dual-functional metamaterial
Item Notation Value length $ l/{\rm{m}} $ $ 0.1 $ cross-sectional area $ A/{\rm{m}}^2$ $ 0.003\;6 $ density of material $ \rho /\left( {{\rm{kg}} \cdot {{\rm{m}}^{ - {\rm{3}}}}} \right) $ $ 1810 $ Young's modulus $E/{\rm{Pa}}$ $ 761\;761 $ radius of spherical cavity $ R/{\rm{m}} $ $ 0.0{\text{2}} $ radius of sliding-ball $r/{\rm{m}}$ $ 0.009 $ density of sliding-ball $ {\rho _{\rm{b}}}/\left( {{\rm{kg}} \cdot {{\rm{m}}^{ - {\rm{3}}}}} \right) $ $ {\text{7780}} $ magnetic flux $B/{\rm{T}} $ $ {\text{0}}{\text{.5}} $ inductance $ {L_{{\rm{ind}}}}/{\rm{H}}$ $ {\text{0}}{\text{.5}} $ coil length $ {L_{{\rm{coil}}}}/{\rm{m}} $ $ {\text{0}}{\text{.1}} $ 
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表 2 试验仪器
Table 2. Experiment instruments
Instruments Version Manufacturer shaker TV-51140 TIRA accelerometer 352C03 PCB vibration controller SCM2E02V SIEMENS
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表 3 带隙内隔振效率
Table 3. Vibration isolation efficiency of band gap
Band-gaps $ {\mu _{{\text{BGIE}}}} $/% local resonant band-gap 59.54 Bragg band-gap 49.39
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