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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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}} $ 表 2 试验仪器
Table 2. Experiment instruments
Instruments Version Manufacturer shaker TV-51140 TIRA accelerometer 352C03 PCB vibration controller SCM2E02V SIEMENS 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 -
[1] 肖峰, 张红艳, 郭少杰等. 多孔压电分流超材料及其带隙特性研究. 应用力学学报, 2019, 38(1): 136-142Xiao Feng, Zhang Hongyan, Guo Shaojie, et al. Study on bandgap characteristics of porous piezoelectric shunt metamaterials. Chinese Journal of Applied Mechanics, 2019, 38(1): 136-142 (in Chinese) [2] 任鑫, 张相玉, 谢亿民. 负泊松比材料和结构的研究进展. 力学学报, 2019, 51(3): 656-687 (Ren Xin, Zhang Xiangyu, Xie Yimin. Research progress in auxetic materials and structures. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 656-687 (in Chinese) doi: 10.6052/0459-1879-18-381 [3] 夏利福, 杨德庆. 含负泊松比超材料肋板的双层圆柱壳声振性能分析. 振动与冲击, 2018, 37(18): 138-144 (Xia Lifu, Yang Deqing. Acoustics and vibration analysis of a double cylindrical shell with lightweight auxetic metamaterial ribs. Journal of Vibration and Shock, 2018, 37(18): 138-144 (in Chinese) [4] 刘少刚, 赵跃超, 赵丹. 基于磁流变弹性体多包覆层声学超材料带隙及传输谱特性. 物理学报, 2019, 68(23): 234301 (Liu Shaogang, Zhao Yuechao, Zhao Dan. Bandgap and transmission spectrum characteristics of multilayered acoustic metamaterials with magnetorheological elastomer. ActaPhysica Sinica, 2019, 68(23): 234301 (in Chinese) doi: 10.7498/aps.68.20191334 [5] 张印, 尹剑飞, 温激鸿等. 基于质量放大局域共振型声子晶体的低频减振设计. 振动与冲击, 2016, 35(17): 26-32Zhang Yin, Yin Jianfei, Wen Jihong, et al. Low frequency vibration reduction design for inertial local resonance phononic crystals based on inertial amplification. Journal of Vibration and Shock, 2016, 35(17): 26-32 (in Chinese)) [6] 沈惠杰, 李雁飞, 苏永生等. 舰船管路系统声振控制技术评述与声子晶体减振降噪应用探索. 振动与冲击, 2017, 36(15): 163-170Shen Huijie, Li Yanfei, Su Yongsheng, et al. Review of sound and vibration control techniques for ship piping systems and exploration of photonic crystals applied in noise and vibration reduction. Journal of Vibration and Shock, 2017, 36(15): 163-170 (in Chinese)) [7] 许振龙, 吴福根, 黄亮国. 局域共振型磁流变隔振支座低频完全禁带研究. 压电与声光, 2015, 37(2): 330-333Xu Zhenlong, Wu Fugen, Huang Liangguo. Study on low – frequency complete band gaps of local resonant magnetorheological vibration isolators. Piezoelectrics & Acoustooptics, 2015, 37(2): 330-333 (in Chinese) [8] 秦浩星, 杨德庆. 声子晶体负泊松比蜂窝基座的减振机理研究. 振动工程学报, 2019, 32(3): 421-430 (Qin Haoxing, Yang Deqing. Vibration reduction mechanism for phononic crystal cellular mount with auxetic effect. Journal of Vibration Engineering, 2019, 32(3): 421-430 (in Chinese) [9] 高南沙, 李沛霖, 周文林等. 四方折叠梁声子晶体低频带隙特性研究. 噪声与振动控制, 2019, 39(1): 210-215 (Gao Nansha, Li Peilin, Zhou Wenlin, et al. Low frequency bandgap characteristics of four-fold-beam phononic crystals. Noise and Vibration Control, 2019, 39(1): 210-215 (in Chinese) [10] 李静茹, 黎胜. 周期新型超材料板多阶弯曲波带隙研究. 振动与冲击, 2018, 37(1): 163-171 (Li Jingru, Li Sheng. Multi-flexural wave band gaps of a new periodic metamaterial plate. Journal of Vibration and Shock, 2018, 37(1): 163-171 (in Chinese) [11] 殷鸣, 江卫锋, 殷国富. 含共振单元的单相3维声子晶体设计及其带隙特性研究. 工程科学与技术, 2020, 52(5): 223-229 (Yin Ming, Jiang Weifeng, Yin Guofu. Design of single phase 3D phononic crystal with resonantor and research of band gap property. Advanced Engineering Sciences, 2020, 52(5): 223-229 (in Chinese) [12] 王伟, 曹军义, 林京等. 一种非线性双稳态人体运动能量俘获技术. 西安交通大学学报, 2015, 49(8): 58-63 (Wang Wei, Cao Junyi, Lin Jing, et al. Nonlinear bi-stable energy harvester from human motion. Journal of Xi'an Jiaotong University, 2015, 49(8): 58-63 (in Chinese) doi: 10.7652/xjtuxb201508010 [13] Hu G, Tang L, Liang J, et al. Acoustic-elastic metamaterials and phononic crystals for energy harvesting: A review. Smart Materials and Structures, 2021, 30(8): 085025 [14] 周生喜, 曹军义, Erturk Alper等. 压电磁耦合振动能量俘获系统的非线性模型研究. 西安交通大学学报, 2014, 48(1): 106-111 (Zhou Shengxi, Cao Junyi, Erturk Alper, et al. Nonlinear model for piezoelectric energy harvester with magnetic coupling. Journal of Xi'an Jiaotong University, 2014, 48(1): 106-111 (in Chinese) [15] 李魁, 杨智春, 谷迎松等. 变势能阱双稳态气动弹性能量收集的性能增强研究. 航空学报, 2020, 41(9): 223710 (Li Kui, Yang Zhichun, Gu Yingsong, et al. Performance enhancement of variable-potential-well bi-stable aeroelasticity energy harvesting. Acta Aeronautica et Astronautica Sinica, 2020, 41(9): 223710 (in Chinese) [16] 曹军义, 任晓龙, 周生喜等. 基于并联电感同步开关控制的振动能量回收方法研究. 振动与冲击, 2012, 31(17): 56-60 (Cao Junyi, Ren Xiaolong, Zhou Shengxi, et al. Vibration energy harvesting based on synchronized switch control of parallel inductor. Journal of Vibration and Shock, 2012, 31(17): 56-60 (in Chinese) doi: 10.3969/j.issn.1000-3835.2012.17.010 [17] 卢一铭, 曹东兴, 申永军等. 局域共振型声子晶体板缺陷态带隙及其俘能特性研究. 力学学报, 2021, 53(4): 1114-1123 (Lu Yiming, Cao Dongxing, Shen Yongjun, et al. Study on the bandgaps of defect states and application of energy harvesting of local resonant phononic crystal plate. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1114-1123 (in Chinese) doi: 10.6052/0459-1879-20-436 [18] 孙伟彬, 王婷, 孙小伟等. 新型二维三组元压电声子晶体板的缺陷态及振动能量回收. 物理学报, 2019, 68(23): 234206Sun Weibin, Wang Ting, Sun Xiaowei, et al. Defect states and vibration energy recovery of novel two-dimensional piezoelectric phononic crystal plate. ActaPhysica Sinica, 2019, 68(23): 234206 (in Chinese) [19] Lu ZQ, Zhao L, Ding H, et al. A dual-functional metamaterial for integrated vibration isolation and energy harvesting. Journal of Sound and Vibration, 2021, 509(29): 116251 [20] Yu DL, Liu YZ, Wang G, et al. Flexural vibration band gaps in Timoshenko beams with locally resonant structures. Journal of Applied Physics, 2006, 100(12): 124901 doi: 10.1063/1.2400803 [21] El-Borgi S, Fernandes R, Rajendran P, et al. Multiple bandgap formation in a locally resonant linear metamaterial beam: Theory and experiments. Journal of Sound and Vibration, 2020, 488: 115647 doi: 10.1016/j.jsv.2020.115647 [22] Hao SM, Wu ZJ, Li FM, et al. Numerical and experimental investigations on the band-gap characteristics of metamaterial multi-span beams. Physics Letters A, 2019, 383(36): 126029 doi: 10.1016/j.physleta.2019.126029 [23] Park S, Jeon W. Ultra-wide low-frequency band gap in a tapered phononic beam. Journal of Sound and Vibration, 2021, 499: 115977 [24] Li ZW, Wang XD. Wave propagation in a dual-periodic elastic metamaterial with multiple resonators. Applied Acoustics, 2021, 172: 107582 doi: 10.1016/j.apacoust.2020.107582 [25] Sharma B, Sun CT. Local resonance and Bragg bandgaps in sandwich beams containing periodically inserted resonators. Journal of Sound and Vibration, 2016, 364: 133-146 doi: 10.1016/j.jsv.2015.11.019 [26] Wang T, Sheng MP, Qin QH. Multi-flexural band gaps in an Euler–Bernoulli beam with lateral local resonators. Physics Letters A, 2016, 380(4): 525-529 doi: 10.1016/j.physleta.2015.12.010 [27] Hu GB, Austin ACM, Sorokin V, et al. Metamaterial beam with graded local resonators for broadband vibration suppression. Mechanical Systems and Signal Processing, 2021, 146: 106982 doi: 10.1016/j.ymssp.2020.106982 [28] Li JY, Gao Y, Huang JP. A bifunctional cloak using transformation media. Journal of Applied Physics. 2010, 108(7): 074504 [29] Shen XY, Li Y, Jiang CR, et al. Thermal cloak-concentrator. Applied Physics Letters, 2016, 109(3): 031907 [30] Maldovan M. Sound and heat revolutions in phononics. Nature, 2013, 503: 209-217 [31] Sugino C, Erturk A. Analysis of multifunctional piezoelectric metastructures for low-frequency bandgap formation and energy harvesting. Journal of Physics D: Applied Physics, 2018, 51(21): 215103 -