The Low-Frequency Broadband Mechanism of Nonlinear Elastic Metamaterials With Gaps
-
摘要:
揭示了基于非线性混沌理论含间隙的非线性局域共振结构的低频宽带形成机理，提出了一类含间隙非线性局域共振结构设计的新理念。在该间隙非线性局域共振系统中，产生了非线性混沌现象，且这种非线性运动可以成功地改变振动噪声中的频谱结构，当系统运动进入混沌状态时，线性谱能量大大削弱，变成了一个连续的宽频谱，进而有效隔离低频线谱。有限元计算结果表明，正是这个间隙引起的非线性混沌现象导致了低频宽带的产生，且理论分析和有限元分析结果高度一致。因此，这类含间隙非线性局域共振弹性超材料结构的设计新思想为局域共振弹性超材料的发展开辟了新天地，且基于非线性混沌理论的低频带隙的形成机理为减振降噪应用研究奠定了非常重要的理论基础。
Abstract:A new formation mechanism of the low-frequency broadband within gapped nonlinear local resonance structures was revealed based on the nonlinear chaos theory, and a novel concept for designing nonlinear local resonant structures with small gaps was further proposed. Due to the small gaps, the nonlinear chaos phenomenon occurs in the local resonance system, which can change the spectrum structure in vibration noise successfully, and the linear spectral energy greatly weakens and a continuous broad spectrum forms after chaotic motion, to effectively isolate the low-frequency spectrum. Most importantly, the finite element results show that, the nonlinearity of the small gap indeed leads to the low-frequency band-gap within the nonlinear local resonance. Therefore, the new idea for designing the nonlinear local resonance structure makes a new way to the development of local resonant elastic metamaterials, and the formation mechanism of low-frequency band-gap based on the nonlinear chaos theory lays a very important theoretical basis for vibration and noise reduction.
-
图 2 不同间隙下m2的相图及基体m1的位移响应频谱图：(a) 间隙为0.065 mm，m2相图；(b) 间隙为0.065 mm，m1频谱图；(c) 间隙为0.062 mm，m2相图；(d) 间隙为0.062 mm，m1频谱图；(e) 间隙为0.05 mm，m2相图；(f) 间隙为0.05 mm，m1频谱图；(g) 间隙为0.013 5 mm，m2相图；(h) 间隙为0.013 5 mm，m1频谱图
Figure 2. Phase diagrams of m2 and displacement response spectra of matrix m1 under different gaps: (a) gap is 0.065 mm, the m2 phase diagram; (b) gap is 0.065 mm, the m1 displacement response spectrum; (c) gap is 0.062 mm, the m2 phase diagram; (d) gap is 0.062 mm, the m1 displacement response spectrum; (e) gap is 0.05 mm, the m2 phase diagram; (f) gap is 0.05 mm, the m1 displacement response spectrum; (g) gap is 0.013 5 mm, the m2 phase diagram; (h) gap is 0.013 5 mm, the m1 displacement response spectrum
图 4 基体m1的位移响应频谱图：(a) 线性系统基体m1的位移响应频谱图；(b) 未混沌状态下非线性系统m1的位移响应频谱图；(c) 混沌状态下非线性系统m1的位移响应频谱图
Figure 4. Displacement response spectrograms of matrix m1: (a) the linear system m1 displacement response spectrum; (b) the displacement response spectrogram of nonlinear system m1 in the unchaotic state; (c) the displacement response spectrogram of nonlinear system m1 in the chaotic state
图 5 局域共振弹性超材料结构：(a) 无间隙局域共振结构单元；(b) 含间隙局域共振结构单元
Figure 5. The local resonance elastic metamaterial structure: (a) the gapless LR structural unit; (b) the gapped LR structural unit
图 7 局域共振结构带隙: (a) 无间隙局域共振结构的带隙；(b) 含间隙非线性局域共振结构的带隙；(c) 图(b)中带隙下界对应的放大图
Figure 7. Local resonance structure band gaps: (a) band gaps of gapless local resonance structures; (b) band gaps of gapped local resonance structures; (c) the enlarged view corresponding to the lower bound of the band gaps in fig. (b)
图 9 非线性局域共振结构的带隙及传输率: (a) 弹性波的透射率；(b) 带隙
Figure 9. Band gaps and transmission rates of nonlinear local resonance structures: (a) the transmissivity of elastic waves; (b) band gaps
图 10 非线性局域共振结构各个点的振型: (a) A点的模态；(b) B点的模态；(c) C点的模态；(d) D点的模态；(e) E点的模态；(f) F点的模态
注 为了解释图中的颜色，读者可以参考本文的电子网页版本。
Figure 10. Mode shapes at various points of nonlinear LR structures: (a) point A modal; (b) point B modal; (c) point C modal; (d) point D modal; (e) point E modal; (f) point F modal
图 11 间隙对非线性局域共振结构带隙的影响
Figure 11. Influences of gaps on the band gaps of nonlinear LR structures
表 1 材料参数
Table 1. Material parameter
material Young’s modulus E/GPa Poisson’s ratio ν density ρ/(kg/m3) silicone rubber 1.2 0.47 1300 plumbum 4.35 0.368 11600 perspex 0.2 0.389 1142 aluminum 7.2 0.35 2730 
下载: 导出CSV
-
[1] MEAD D J, MEADOR D. Passive Vibration Control[M]. Chichester: Wiley, 1998. [2] HARRIS C M, PIERSOL A G. Harris’ Shock and Vibration Handbook[M]. New York: Mc Graw-Hill, 2002. [3] RIVIN E I. Passive Vibration Isolation[M]. New York: ASME Press, 2003. [4] CHI W, MA S J, SUN J Q. A hybrid multi-degree-of-freedom vibration isolation platform for spacecrafts by the linear active disturbance rejection control[J]. Applied Mathematics and Mechanics (English Edition) , 2020, 41(5): 805-818. doi: 10.1007/s10483-020-2606-5 [5] 唐斯密, 赵存生, 朱石坚, 等. 刚度分段线性系统隔振抗冲击优化设计研究[J]. 噪声与振动控制, 2011, 31(1): 27-32. (TANG Simi, ZHAO Cunsheng, ZHU Shijian, et al. Study on optimal design for vibration and shock isolation of piecewise linear stiffness system[J]. Noise and Vibration Control, 2011, 31(1): 27-32.(in Chinese) doi: 10.3969/j.issn.1006-1355-2011.01.005 [6] 管延峰. 柔性基础多支承非线性隔振系统动力学分析[D]. 硕士学位论文. 济南: 山东大学, 2013.GUAN Yanfeng. Nonlinear dynamic analysis of multi-supported vibration isolation system on felxible foundation[D]. Master Thesis. Jinan: Shandong University, 2013. (in Chinese) [7] 徐道临, 吕永建, 周加喜, 等. 非线性隔振系统动力学特性分析的FFT多谐波平衡法[J]. 振动与冲击, 2012, 31(22): 39-44. (XU Daolin, LÜ Yongjian, ZHOU Jiaxi, et al. FFT multi-harmonic balance method for dynamic analysis of a nonlinear vibration isolation system[J]. Journal of Vibration and Shock, 2012, 31(22): 39-44.(in Chinese) doi: 10.3969/j.issn.1000-3835.2012.22.008 [8] 郝志峰. 基于高性能低频隔振器的动力学与振动控制研究[D]. 博士学位论文. 哈尔滨: 哈尔滨工业大学, 2016.HAO Zhifeng. Research on dynamics and vibration control based upon high-performance low-frequency isolator[D]. PhD Thesis. Harbin: Harbin Institute of Technology, 2016. (in Chinese) [9] 孟令帅, 孙景工, 牛福, 等. 新型准零刚度隔振系统的设计与研究[J]. 振动与冲击, 2014, 33(11): 195-199. (MENG Lingshuai, SUN Jinggong, NIU Fu, et al. Design and analysis of a level quasi-zero stiffness vibration isolation system[J]. Journal of Vibration and Shock, 2014, 33(11): 195-199.(in Chinese) [10] 赵建学, 俞翔, 柴凯, 等. 柔性基础准零刚度隔振系统全局性态分析[J]. 噪声与振动控制, 2019, 37(3): 19-23. (ZHAO Jianxue, YU Xiang, CHAI Kai, et al. Global behavior analysis of the quasi-zero stiffness vibration isolation system with flexible foundation[J]. Noise and Vibration Control, 2019, 37(3): 19-23.(in Chinese) [11] 李万祥, 张永燕. 一类四自由度系统碰撞问题[J]. 工程力学, 2013, 30(9): 259-263. (LI Wanxiang, ZHANG Yongyan. Collision problem of a four-degree-of-freedom vibro-impact system[J]. Engineering Mechanics, 2013, 30(9): 259-263.(in Chinese) doi: 10.6052/j.issn.1000-4750.2011.12.0847 [12] 张永燕. 多自由度碰撞系统的动力学研究[D]. 硕士学位论文. 兰州: 兰州交通大学, 2012.ZHANG Yongyan. Research on dynamics of multiple-degree-of-freedom in vibro-impact system[D]. Master Thesis. Lanzhou: Lanzhou Jiaotong University, 2012. (in Chinese) [13] 吴波, 艾星然. 准零刚度悬架的低频隔振仿真分析[J]. 噪声与振动控制, 2021, 41(3): 127-134. (WU Bo, AI Xingran. Simulation analysis of low-frequency vibration isolation of quasi-zero stiffness suspensions[J]. Noise and Vibration Control, 2021, 41(3): 127-134.(in Chinese) doi: 10.3969/j.issn.1006-1355.2021.03.022 [14] 吴明亮, 赵晨名, 张来喜. 准零刚度振动控制系统的研究进展[J]. 南京理工大学学报(自然科学版), 2021, 45(1): 18-26. (WU Mingliang, ZHAO Chenming, ZHANG Laixi. Research progress of quasi-zero stiffness vibration control system[J]. Journal of Nanjing University of Science and Technology, 2021, 45(1): 18-26.(in Chinese) [15] 肖庆雨, 周加喜, 徐道临, 等. 一种六自由度准零刚度隔振平台[J]. 振动与冲击, 2019, 38(1): 258-264.XIAO Qingyu, ZHOU Jiaxi, XU Daolin, et al. A 6-DOF quai-zero stiffness vibration isolation platform[J]. Journal of Vibration and Shock, 2019, 38(1): 258-264. (in Chinese) [16] FANG X, WEN J, BONELLO B, et al. Ultra-low and ultra-broad-band nonlinear acoustic metamaterials[J]. Nature Communications, 2017, 8(1): 1288. doi: 10.1038/s41467-017-00671-9 [17] 方鑫. 非线性声学超材料中弹性波传播理论及其减振应用研究[D]. 博士学位论文. 长沙: 国防科技大学, 2018.FANG Xin. Nonlinear acoustic metamaterials: theory of elastic wave propagation and applications on vibration reduction[D]. PhD Thesis. Changsha: National University of Defense Technology, 2018. (in Chinese) [18] 代显智, 张章, 刘小亚, 等. 非线性宽频振动能量采集技术的研究进展[J]. 中国科学: 技术科学, 2016, 46(8): 791-807. (DAI Xianzhi, ZHANG Zhang, LIU Xiaoya, et al. Research progress of nonlinear broadband vibration energy harvesting technology[J]. Scientia Sinica: Technologica, 2016, 46(8): 791-807.(in Chinese) doi: 10.1360/N092015-00227 [19] NESTERENKO V F. Dynamics of Heterogeneous Materials Materials[M]. New York: Springer, 2001. [20] ALIJANI F, AMABILI M. Nonlinear vibrations and multiple resonances of fluid filled arbitrary laminated circular cylindrical shells[J]. Composite Structures, 2014, 108: 951-962. doi: 10.1016/j.compstruct.2013.10.029 [21] HIGASHIYAMA N, DIO Y, NAKATANI A. Nonlinear dynamics of a model of acoustic metamaterials with local resonators[J]. Nonlinear Theory and Its Applications, 2016, 8(2): 129-145. [22] CVETICANIN L, ZUKOVIC M. Negative effective mass in acoustic metamaterial with nonlinear mass-in-mass subsystems[J]. Communications Nonlinear Science Numerical Simulation, 2017, 51: 89-104. doi: 10.1016/j.cnsns.2017.03.017 -
计量
- 文章访问数: 692
- HTML全文浏览量: 415
- PDF下载量: 72
- 被引次数: 0
渝公网安备50010802005915号