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Structural vibration is commonly seen in engineering, which can cause resonance and fatigue damage in structure. Therefore, it is very desirable in vibration control techniques to achieve structure with low-frequency and broadband damping feature. In this paper, we design a phononic crystal (PC) beam with X-shaped locally resonant metadamping (X-LRMD) structures. Based on the PC theory, the flexural wave propagation in X-LRMD beam is studied. The equivalent dynamic properties of the X LRMD structure are analyzed by Lagrange equation. It is shown that due to its geometric nonlinearity, the X LRMD can effectively increase the damping of the system, which is validated by the transfer matrix method. The influence of structural parameters of X LRMD on band gap characteristics of the PC beam is then discussed in detail by using the finite element method with COMSOL multiphysics software in conjunction with Matlab, where the PC beam with X LRMD is modeled with the multi-body dynamic module within COMSOL and the band gap characteristics are calculated. The damping properties of the system are studied also using the finite element method. It is shown that compared with the equivalent structures, the PC beam with X LRMD can magnify the damping of the structure system, demonstrating a meta-damping phenomenon. The X LRMD in the PC beam can not only generate lower frequency and wider range band gaps but also suppress the vibration in passband ranges. This can bring a new design for reducing the vibration of structural systems.
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Keywords:
- phononic crystals /
- band gap /
- metadamping /
- geometric nonlinearity
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[5] Shu H S, Zhang F, Liu S G, Gao E W, Li S D 2014 J. Vib. Shock 33 147 (in Chinese) [舒海生, 张法, 刘少刚, 高恩武, 李世丹 2014 振动与冲击 33 147]
[6] Ma G C, Fu C X, Wang G H, Hougne del P, Christensen J, Lai Y, Sheng P 2016 Nat. Commun. 7 13536
[7] Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 1734
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[14] Nouh M, Aldraihen O, Baz A 2015 J. Sound Vib. 341 53
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[16] Wu Q, Ling D S, Xu X 1997 J. Zhejiang Univ. - Sci. A 4 462 (in Chinese) [吴强, 凌道盛, 徐兴 1997 浙江大学学报 4 462]
[17] Wu X, Yang L J 2008 J. Vib. Shock 2 771 (in Chinese) [吴晓, 杨立军 2008 振动与冲击 2 771]
[18] Liu C C, Jing X J, Li F M 2015 Int. J. Mech. Sci. 98 169
[19] Sun X T, Jing X J 2015 Mech. Syst. Signal Pr. 62 149
[20] Sun X T, Jing X J 2016 Mech. Syst. Signal Pr. 80 166
[21] Sun X T, Jing X J, Xu J, Cheng L 2014 J. Sound Vib. 333 2404
[22] Huang Y Y, Zhao Y G, Zhao W D 2011 J. Qinghai Univ. 2 912 (in Chinese) [黄永玉, 赵永刚, 赵伟东 2011 青海大学学报 2 912]
[23] Manimala J M, Huang H H, Sun C T, Snyder R, Bland S 2014 Eng. Struct. 80 458
[24] Wang Z F 2001 J. Shandong Univ. Technol. 1 51 (in Chinese) [王振发 2001 齐鲁工业大学学报 1 51]
[25] Wang G, Wen J H, Wen X S, Yu D L, Liu Y Z 2005 Chin. J. Mech. 41 107 (in Chinese) [王刚, 温激鸿, 温熙森, 郁殿龙, 刘耀宗 2005 机械工程学报 41 107]
[26] Li L, Liu Y Z, Yu D L 2006 J. Vib. Shock 25 632 (in Chinese) [李黎, 刘耀宗, 郁殿龙 2006 振动与冲击 25 632]
[27] Wen Q H, Zuo S G, Wei H 2012 Acta Phys. Sin. 61 034301 (in Chinese) [文岐华, 左曙光, 魏欢 2012 61 034301]
[28] Zhang Y F 2014 M. S. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [张亚峰 2014 硕士学位论文 (长沙: 国防科学技术大学)]
[29] Zhang H, Wen J H, Xiao Y, Wang G, Wen X S 2015 J. Sound Vib. 343 104
[30] Zhang H, Xiao Y, Wen J H, Yu D L, Wen X S 2016 Appl. Phys. Lett. 108 1734
[31] Mei J, Ma G, Yang M, Yang Z, Wen W, Sheng P 2012 Nat. Commun. 3 132
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[1] Ding W J 2014 Damping Theory (Beijing: Tsinghua Press) pp1-4 (in Chinese) [丁文镜 2014 减振理论(北京: 清华大学出版社) 第1-4页]
[2] Silva C W (translated by Li H B, Zhang M) 2013 Vibration Damping, Control and Design (Beijing: Mechanical Industry Press) pp243-246 (in Chinese) [Silva C W著 (李惠彬, 张曼 译) 2013振动阻尼、控制和设计 (北京: 机械工业出版社) 第243-246页]
[3] Wen X S 2006 Theory and Technology of Photonic/Phononic Crystals (Beijing: Science Press) pp5-7 (in Chinese) [温熙森 2006 光子/声子晶体理论与技术(北京: 科学出版社) 第5-7页]
[4] Wen X S, Wen J H, Yu D L, et al. 2009 Photonic Crystal (Beijing: National Defence Industry Press) pp8-10 (in Chinese) [温熙森, 温激鸿, 郁殿龙 等 2009 声子晶体(北京: 国防工业出版社) 第8-10页]
[5] Shu H S, Zhang F, Liu S G, Gao E W, Li S D 2014 J. Vib. Shock 33 147 (in Chinese) [舒海生, 张法, 刘少刚, 高恩武, 李世丹 2014 振动与冲击 33 147]
[6] Ma G C, Fu C X, Wang G H, Hougne del P, Christensen J, Lai Y, Sheng P 2016 Nat. Commun. 7 13536
[7] Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 1734
[8] Wu J H, Zhang S W, Shen L 2013 Chin. J. Mech. 49 62 (in Chinese) [吴九汇, 张思文, 沈礼 2013 机械工程学报 49 62]
[9] Zhang Y, Yin J F, Wen J H, Yu D L 2016 J. Vib. Shock 35 26 (in Chinese) [张印, 尹剑飞, 温激鸿, 郁殿龙 2016 振动与冲击 35 26]
[10] Zhang J L, Yao H, Du J, Zhao J B, Dong Y K 2016 Bull. Chin. Ceram. Soc. 35 2767 (in Chinese) [张佳龙, 姚宏, 杜军, 赵静波, 董亚科 2016 硅酸盐通报 35 2767]
[11] Qi P S, Du J, Jiang J L, Dong Y K, Zhang J L 2016 J. Synthetic Cryst. 45 1094 (in Chinese) [祁鹏山, 杜军, 姜久龙, 董亚科, 张佳龙 2016 人工晶体学报 45 1094]
[12] Chen L, Wu W G, Zhou R 2016 Tech. Acoust. 35 222 (in Chinese) [陈琳, 吴卫国, 周榕 2016 声学技术 35 222]
[13] Hussein M I, Frazier M J 2013 J. Sound Vib. 332 4767
[14] Nouh M, Aldraihen O, Baz A 2015 J. Sound Vib. 341 53
[15] Frazier M J, Hussein M I 2015 J. Acoust. Soc. Am. 138 3169
[16] Wu Q, Ling D S, Xu X 1997 J. Zhejiang Univ. - Sci. A 4 462 (in Chinese) [吴强, 凌道盛, 徐兴 1997 浙江大学学报 4 462]
[17] Wu X, Yang L J 2008 J. Vib. Shock 2 771 (in Chinese) [吴晓, 杨立军 2008 振动与冲击 2 771]
[18] Liu C C, Jing X J, Li F M 2015 Int. J. Mech. Sci. 98 169
[19] Sun X T, Jing X J 2015 Mech. Syst. Signal Pr. 62 149
[20] Sun X T, Jing X J 2016 Mech. Syst. Signal Pr. 80 166
[21] Sun X T, Jing X J, Xu J, Cheng L 2014 J. Sound Vib. 333 2404
[22] Huang Y Y, Zhao Y G, Zhao W D 2011 J. Qinghai Univ. 2 912 (in Chinese) [黄永玉, 赵永刚, 赵伟东 2011 青海大学学报 2 912]
[23] Manimala J M, Huang H H, Sun C T, Snyder R, Bland S 2014 Eng. Struct. 80 458
[24] Wang Z F 2001 J. Shandong Univ. Technol. 1 51 (in Chinese) [王振发 2001 齐鲁工业大学学报 1 51]
[25] Wang G, Wen J H, Wen X S, Yu D L, Liu Y Z 2005 Chin. J. Mech. 41 107 (in Chinese) [王刚, 温激鸿, 温熙森, 郁殿龙, 刘耀宗 2005 机械工程学报 41 107]
[26] Li L, Liu Y Z, Yu D L 2006 J. Vib. Shock 25 632 (in Chinese) [李黎, 刘耀宗, 郁殿龙 2006 振动与冲击 25 632]
[27] Wen Q H, Zuo S G, Wei H 2012 Acta Phys. Sin. 61 034301 (in Chinese) [文岐华, 左曙光, 魏欢 2012 61 034301]
[28] Zhang Y F 2014 M. S. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [张亚峰 2014 硕士学位论文 (长沙: 国防科学技术大学)]
[29] Zhang H, Wen J H, Xiao Y, Wang G, Wen X S 2015 J. Sound Vib. 343 104
[30] Zhang H, Xiao Y, Wen J H, Yu D L, Wen X S 2016 Appl. Phys. Lett. 108 1734
[31] Mei J, Ma G, Yang M, Yang Z, Wen W, Sheng P 2012 Nat. Commun. 3 132
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