二自由度振子型的二维LR声子晶体弯曲振动带隙研究
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摘要
为了抑制板件的低频振动,提出了一种由二自由度振子周期性排列的二维LR (Locally Resonant)声子晶体,实现了低频范围内的双带隙。运用平面波展开法计算了该声子晶体结构的带隙特性,并通过有限元法和样件试验得到的振动传递特性验证了带隙计算结果的准确性。通过对含二自由度振子的元胞模态振型计算,进一步揭示了该结构低频双带隙的产生机理;振子的平动和转动的两种振型相互耦合作用可以形成两个低频弯曲波带隙,并根据简化模型推导出双带隙起始和截止频率计算方法;分析了弹簧刚度、弹簧距离、振子质量和转动惯量对双带隙的影响。结果表明,通过合理选择设计参数可以获得低频范围内的双带隙特性,为声子晶体在汽车板件多频减振的应用研究上提供了新的方法。
In order to suppress the vibration of plate components in low frequency, a two-dimensional locally resonant phononic crystal with dual band gaps was proposed. The oscillators with two degrees of freedom were connected to the plate in a periodic arrangement. The plane wave expansion method(PWEM) was used to calculate the band structure. The finite element method(FEM) and experiments were also applied to acquire the vibration transmission spectrums and verify the accuracy of the theoretical calculation. The modal analysis based on a simplified model was carried out in order to reveal the mechanism of the dual band gaps in low frequency. The coupling action between the oscillators' translation and rotation gives rise to form the dual flexural wave band gaps. Based on the simplified model, an approach was proposed to calculate the start and stop frequencies of band gaps. The results are consistent with the band gaps calculated by the PMEM. The influences of the spring' s stiffness and interval, oscillators' mass and moment of inertia on dual band gaps were investigated. The target dual band gaps can be obtained through selecting appropriate parameters of the model. The method provides references to the application of phononic crystals in vehicle panels.
In order to suppress the vibration of plate components in low frequency, a two-dimensional locally resonant phononic crystal with dual band gaps was proposed. The oscillators with two degrees of freedom were connected to the plate in a periodic arrangement. The plane wave expansion method(PWEM) was used to calculate the band structure. The finite element method(FEM) and experiments were also applied to acquire the vibration transmission spectrums and verify the accuracy of the theoretical calculation. The modal analysis based on a simplified model was carried out in order to reveal the mechanism of the dual band gaps in low frequency. The coupling action between the oscillators' translation and rotation gives rise to form the dual flexural wave band gaps. Based on the simplified model, an approach was proposed to calculate the start and stop frequencies of band gaps. The results are consistent with the band gaps calculated by the PMEM. The influences of the spring' s stiffness and interval, oscillators' mass and moment of inertia on dual band gaps were investigated. The target dual band gaps can be obtained through selecting appropriate parameters of the model. The method provides references to the application of phononic crystals in vehicle panels.
引文
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[18] ZHAO H J,GUO H W,GAO M X,et al.Vibration band gaps in double-vibrator pillared phononic crystal plate[J].Journal of Applied Physics,2016,119(1):014903.
[19] 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 Xudong,ZUO Shuguang,NI Tianxin,et al.Study of the band gap characteristics of a locally resonant phononic crystal beam with attached double oscillators in parallel[J].Journal of Vibration Engineering,2017,30(1):79-85.
[20] 左曙光,黄海东,吴旭东,等.基于声子晶体及其缺陷态特性的车内降噪方法[J].汽车工程,2017,39(5):569-574.ZUO Shuguang,HUANG Haidong,WU Xudong,et al.Interior noise reduction scheme based on phononic crystal and its defect characteristics[J].Automotive Engineering,2017,39(5):569-574.
[2] 左曙光,谭钦文,孙庆,等.声子晶体梁在燃料电池车副车架减振中的应用研究[J].振动与冲击,2013,32(18):26-30.ZUO Shuguang,TAN Qinwen,SUN Qing,et al.Vibration reduction with phononic crystals beams for subframe of a fuel-cell car[J].Journal of Vibration and Shock,2013,32(18):26-30.
[3] KUSHWAHA M S,HAILEVI P,DOBRZYNSKI L,et al.Acoustic band structure of periodic elastic composites[J].Physical Review Letters,1993,71(13):2022.
[4] LIU Z,ZHANG X,MAO Y,et al.Locally resonant sonic materials[J].Science,2000,289(5485):1734-1736.
[5] 郑玲,李以农.一维声子晶体的振动特性与实验研究[J].振动工程学报,2007,20(4):417-421.ZHENG Ling,LIU Yinong.Theoretical and experimental study on the characteristics of wave propagation for one dimensional phononic crystal [J].Journal of Vibration Engineering,2007,20(4):417-421.
[6] YU D,LIU Y,WANG G,et al.Flexural vibration band gaps in Timoshenko beams with locally resonant structures[J].Journal of Applied Physics,2006,100(12):124901.
[7] WANG T,SHENG M P,GUO Z W,et al.Acoustic characteristics of damped metamaterial plate with parallel attached resonators[J].Archives of Mechanics,2017,69(1):29-52.
[8] XIAO Y,WEN J,WEN X.Flexural wave band gaps in locally resonant thin plates with periodically attached spring-mass resonators[J].Journal of Physics D:Applied Physics,2012,45(19):195401.
[9] XIAO Y,WEN J,WANG G,et al.Theoretical and experimental study of locally resonant and bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators [J].Journal of Vibration and Acoustics,2013,135(4):041006.
[10] OUDICH M,LI Y,ASSOUAR B M,et al.A sonic band gap based on the locally resonant phononic plates with stubs[J].New Journal of Physics,2010,12(8):083049.
[11] HSU J C.Local resonances-induced low-frequency band gaps in two-dimensional phononic crystal slabs with periodic stepped resonators[J].Journal of Physics D:Applied Physics,2011,44(5):055401.
[12] BADREDDINE ASSOUAR M,OUDICH M.Enlargement of a locally resonant sonic band gap by using double-sides stubbed phononic plates[J].Applied Physics Letters,2012,100(12):123506.
[13] PENG H,PAI P F,DENG H.Acoustic multi-stopband metamaterial plates design for broadband elastic wave absorption and vibration suppression[J].International Journal of Mechanical Sciences,2015,103:104-114.
[14] PENG H,PAI P F.Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression[J].International Journal of Mechanical Sciences,2014,89:350-361.
[15] 钱堃.电动汽车声品质评价分析与控制技术研究 [D].长春:吉林大学,2016.
[16] 舒海生,高恩武,刘少刚,等.声子晶体串联组合杆振动带隙研究[J].振动与冲击,2014,33(16):194-200.SHU Haisheng,GAO Enwu,LIU Shaogang,et al.Vibration band gaps of a kind of serial combined rod of phononic crystals[J].Journal of Vibration and Shock,2014,33(16):194-200.
[17] WANG Z,ZHANG P,ZHANG Y.Locally resonant band gaps in flexural vibrations of a Timoshenko beam with periodically attached multioscillators[J].Mathematical Problems in Engineering,2013,2013:388-400.
[18] ZHAO H J,GUO H W,GAO M X,et al.Vibration band gaps in double-vibrator pillared phononic crystal plate[J].Journal of Applied Physics,2016,119(1):014903.
[19] 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 Xudong,ZUO Shuguang,NI Tianxin,et al.Study of the band gap characteristics of a locally resonant phononic crystal beam with attached double oscillators in parallel[J].Journal of Vibration Engineering,2017,30(1):79-85.
[20] 左曙光,黄海东,吴旭东,等.基于声子晶体及其缺陷态特性的车内降噪方法[J].汽车工程,2017,39(5):569-574.ZUO Shuguang,HUANG Haidong,WU Xudong,et al.Interior noise reduction scheme based on phononic crystal and its defect characteristics[J].Automotive Engineering,2017,39(5):569-574.