声子晶体负泊松比蜂窝基座的减振机理研究
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摘要
通过建立声子晶体负泊松比蜂窝基座的等效动力学模型,研究该基座局域共振减振机理。探讨动力学参数(固有频率比、质量比、阻尼比)、声子晶体的周期层数等对基座减振性能的影响规律。研究结果表明,当声子晶体固有频率与基座固有频率接近时,能有效降低基座发生结构共振时的响应幅值。建立声子晶体蜂窝基座的优化设计模型,优化得到具有指定局域共振固有频率的声子晶体结构。动力学频响计算表明,该优化设计基座能够有效抑制结构的低频共振现象。
In this paper,the local resonance reduction mechanism of phononic crystal cellular mount with auxetic effects is studied by establishing the dynamic model.The influence of the dynamic parameters(natural frequency ratio,mass ratio and damping ratio)on the vibration reduction performance of this mount is analyzed.It was shown that the frequency response of the cellular mount in the vicinity of the resonant frequency can be effectively reduced when the natural frequency of the phononic crystal is close to the natural frequency of the cellular mount.Then,the optimization design model of the phononic crystal auxetic cellular mount is established,and the phononic crystal structure with the specified local resonant frequency is obtained.The dynamic frequency response characteristics of this novel mount are calculated,which shows that the novel mount has better vibration reduction performance in low frequency resonance.
In this paper,the local resonance reduction mechanism of phononic crystal cellular mount with auxetic effects is studied by establishing the dynamic model.The influence of the dynamic parameters(natural frequency ratio,mass ratio and damping ratio)on the vibration reduction performance of this mount is analyzed.It was shown that the frequency response of the cellular mount in the vicinity of the resonant frequency can be effectively reduced when the natural frequency of the phononic crystal is close to the natural frequency of the cellular mount.Then,the optimization design model of the phononic crystal auxetic cellular mount is established,and the phononic crystal structure with the specified local resonant frequency is obtained.The dynamic frequency response characteristics of this novel mount are calculated,which shows that the novel mount has better vibration reduction performance in low frequency resonance.
引文
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[21]吴旭东,左曙光,倪天心,等.并联双振子声子晶体梁结构带隙特性研究[J].振动工程学报,2017,30(1):79-85.Wu Xu-dong,Zuo Shu-guang,Ni Tian-xin,et al.Study of the bandgap characteristics of a locally resonant phononic crystal beam with attached double oscillators in parallel[J].Journal of Vibration Engineering,2017,30(1):79-85.
[22]Liu Z,Zhang X,Mao Y,et al.Locally resonant sonic materials[J].Science,2000,289(5485):1734-1736.
[23]Xiao Y,Mace B R,Wen J H,et al.Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators[J].Physics Letters A,2011,375(12):1485-1491.
[24]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[J].振动与冲击,2016,35(17):26-32.Zhang Yin,Yin Jianfei,Wen Jihong,et al.Low frequency vibration reduction design for inertial local resonance phononic crystals based on inertial amplification[J].Journal of Vibration and Shock,2016,35(17):26-32.
[25]Baravelli E,Carrara M,Ruzzene M.High stiffness,high damping chiral metamaterial assemblies for lowfrequency applications[C]. Health Monitoring of Structural&Biological Systems,International Society for Optics and Photonics,2013.
[26]Baravelli E,Ruzzene M.Internally resonating lattices for bandgap generation and low-frequency vibration control[J].Journal of Sound&Vibration,2013,332(25):6562-6579.
[27]张佳龙,姚宏,杜军,等.基于局域共振型声子晶体在机舱内低频隔声特性[J].硅酸盐学报,2016,44(10):1440-1445.Zhang Jialong,Yao Hong,Du Jun,et al.Low frequency sound insulation characteristics of the locally resonant phononic crystals in the large aircraft cabin[J].Journal of Chinese Ceramic Society,2016,44(10):1440-1445.
[28]Lai Y,Wu Y,Sheng P,et al.Hybrid elastic solids[J].Nature Materials,2011,10(8):620-624.
[29]Mei J,Ma G,Yang M,et al.Dark acoustic metamaterials as super absorbers for low-frequency sound[J].Nature Communications,2012,3(3):756-762.
[30]秦浩星,杨德庆,张相闻.负泊松比声学超材料基座的减振性能研究[J].振动工程学报,2017,30(6):1012-1021.Qin Haoxing,Yang Deqing,Zhang Xiangwen.Vibration reduction of auxetic acoustic metamaterial mount[J].Journal of Vibration Engineering,2017,30(6):1012-1021.
[2]吕林华,杨德庆.船舶钢-复合材料组合基座减振设计方法分析[J].上海交通大学学报,2012,46(8):1196-1202.Lv Linhua,Yang Deqing.Study on vibration reduction design of steel-composite materials hybrid mounting for ships[J].Journal of Shanghai Jiaotong University,2012,46(8):1196-1202.
[3]杨德庆,谢小龙,郭万涛.钢-复合材料组合结构材料选型优化设计映射解法[J].应用力学学报,2011,28(01):29-34.Yang Deqing,Xie Xiaolong,Guo Wantao.Mapping function method for hybrid steel-composite materialsstructure selection optimization design[J].Chinese Journal of Applied Mechanics,2011,28(01):29-34.
[4]谢天宇,王永生,付建,等.含阻尼层基座的加筋柱壳振动及声辐射计算[J].武汉理工大学学报(交通科学与工程版),2013,37(4):878-881.Xie Tianyu,Wang Yongsheng,Fu Jian,et al.Computation of vibration and sound radiation from cylindrical shells with frame coated by damping layer[J].Journal of Wuhan University of Technology(Transportation Science&Engineering),2013,37(4):878-881.
[5]计方,姚熊亮.舰船高传递损失基座振动波传递特性[J].工程力学,2011,28(3):240-244.Ji Fang,Yao Xiongliang.The characteristics of vibration wave propagation from ship high transmission loss base structures[J].Engineering Mechanics,2011,28(3):240-244.
[6]江国和,薛彬,冯伟,等.舰用变压器冲击响应计算[J].噪声与振动控制,2010,29(3):108-112.Jiang Guohe,Xue Bin,Feng Wei,et al.Ship transformer shock response calculation[J].Noise and Vibration Control,2010,29(3):108-112.
[7]张相闻,杨德庆.船用新型抗冲击隔振蜂窝基座[J].振动与冲击,2015,34(10):40-45.Zhang Xiang-wen,Yang De-qing.A novel marine impact resistance and vibration isolation cellular base[J].Journal of Vibration and Shock,2015,34(10):40-45.
[8] Victor S,Tanchum W.On the feasibility of introducing auxetic behavior into thin-walled structures[J].Acta Materialia,2008,57(1):125-135.
[9]卢子兴,赵亚斌.一种有负泊松比效应的二维多胞材料力学模型[J].北京航空航天大学学报,2006,32(5):594-597.Lu Zixing,Zhao Yabin.Mechanical model of two-dimensional cellular materials with negative Poisson’s ratio[J].Journal of Beijing University of Aeronautics and Astronautics,2006,32(5):594-597.
[10]Horrigan E J,Smith C W,Scarpa F L,et al.Simulated optimization of disordered structures with negative Poisson’s ratios[J].Mechanics of Materials,2013,41(8):919-927.
[11]Gibson L J,Ashby M F.Cellular solids:Structure and properties[M].2nd ed.Cambridge:Cambridge University Press,1997.
[12]李永强,李锋,何永亮.四边固支铝基蜂窝夹层板弯曲自由振动分析[J].复合材料学报,2011,28(3):210-216.Li Yongqiang,Li Feng,He Yongliang.Flexural vibration analysis of honeycomb sandwich plate with complete clamped support[J].Acta Materiae Compositae Sinica,2011,28(3):210-216.
[13]李永强,李洁,李锋,等.四边固支对称蜂窝夹层板主共振非线性动力学计算[J].复合材料学报,2012,29(6):179-186.Li Yongqiang,Li Jie,Li Feng,et al.Primary resonance of the symmetric rectangular honeycomb sandwich panels with compleed damped supported boundaries[J].Acta Materiae Compositae Sinica,2012,29(6):179-186.
[14]Hnig A,Stronge W J.In-plane dynamic crushing of honeycomb.Part I:Crush band initiation and wave trapping[J].International Journal of Mechanical Sciences,2002,44(8):1665-1696.
[15]Banerjee S,Bhaskar A.Free vibration of cellular structures using continuum modes[J].Journal of Sound and Vibration,2005,287(l-2):77-100.
[16]Hayes A M,Wang A J,Dempsey B M,et al.Mechanics of linear cellular alloys[J].Mechanics of Materials,2004,36(8):691-713.
[17]Zhang X W,Yang D Q.Numerical and experimental studies of a light-weight auxetic cellular vibration isolation base[J].Shock and Vibration,2016,2016(9):1-16.
[18]Zhang X,Yang D.Mechanical properties of auxetic cellular material consisting of re-entrant hexagonal honeycombs[J].Materials,2016,9(11):900.
[19]Pennec Y,Djafari-Rouhani B,Larabi H.et al.Low frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate[J].Physical Review B,2008,78:104105.
[20]Diaz-De-Anda A,Pimentel A,Flores J,et al.Locally periodic Timoshenko rod:Experiment and theory[J].Journal of the Acoustical Society of America,2005,117(5):2814-2819.
[21]吴旭东,左曙光,倪天心,等.并联双振子声子晶体梁结构带隙特性研究[J].振动工程学报,2017,30(1):79-85.Wu Xu-dong,Zuo Shu-guang,Ni Tian-xin,et al.Study of the bandgap characteristics of a locally resonant phononic crystal beam with attached double oscillators in parallel[J].Journal of Vibration Engineering,2017,30(1):79-85.
[22]Liu Z,Zhang X,Mao Y,et al.Locally resonant sonic materials[J].Science,2000,289(5485):1734-1736.
[23]Xiao Y,Mace B R,Wen J H,et al.Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators[J].Physics Letters A,2011,375(12):1485-1491.
[24]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[J].振动与冲击,2016,35(17):26-32.Zhang Yin,Yin Jianfei,Wen Jihong,et al.Low frequency vibration reduction design for inertial local resonance phononic crystals based on inertial amplification[J].Journal of Vibration and Shock,2016,35(17):26-32.
[25]Baravelli E,Carrara M,Ruzzene M.High stiffness,high damping chiral metamaterial assemblies for lowfrequency applications[C]. Health Monitoring of Structural&Biological Systems,International Society for Optics and Photonics,2013.
[26]Baravelli E,Ruzzene M.Internally resonating lattices for bandgap generation and low-frequency vibration control[J].Journal of Sound&Vibration,2013,332(25):6562-6579.
[27]张佳龙,姚宏,杜军,等.基于局域共振型声子晶体在机舱内低频隔声特性[J].硅酸盐学报,2016,44(10):1440-1445.Zhang Jialong,Yao Hong,Du Jun,et al.Low frequency sound insulation characteristics of the locally resonant phononic crystals in the large aircraft cabin[J].Journal of Chinese Ceramic Society,2016,44(10):1440-1445.
[28]Lai Y,Wu Y,Sheng P,et al.Hybrid elastic solids[J].Nature Materials,2011,10(8):620-624.
[29]Mei J,Ma G,Yang M,et al.Dark acoustic metamaterials as super absorbers for low-frequency sound[J].Nature Communications,2012,3(3):756-762.
[30]秦浩星,杨德庆,张相闻.负泊松比声学超材料基座的减振性能研究[J].振动工程学报,2017,30(6):1012-1021.Qin Haoxing,Yang Deqing,Zhang Xiangwen.Vibration reduction of auxetic acoustic metamaterial mount[J].Journal of Vibration Engineering,2017,30(6):1012-1021.