蜂窝状声子晶体带隙特性及隔振性能
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摘要
设计了一种蜂窝结构声子晶体。用有限元法进行了分析,计算其能带结构图,分析几种振动模式,并阐明带隙机理;针对第一带隙和截止频率的振动模式分别建立等效模型;通过计算不同结构参数的晶体结构的能带图探讨了结构参数对带隙的影响,同时验证了等效模型的合理性,并给出了频率传递曲线。结果表明:该结构为局部共振声子晶体,在36.27～246.91 Hz频率范围内存在1个较宽的带隙。通过改变结构参数,可以进一步拓宽结构带隙,并且降低带隙频率。通过优化结构,当频率包含在间隙范围内时,可以实现121.86 dB的振动衰减。研究结果为声子晶体结构的设计提供了参考。
A kind of honeycomb structure phononic crystal was designed, and analyzed by finite element method. Its band structure diagram was calculated, and several vibration modes were analyzed to elucidate the bandgaps mechanism. Equivalent models were established for the vibration modes of the first bandgap and the cut-off frequency, respectively. The effect of structural parameters on the bandgap was investigated though calculating the energy band diagrams of crystal structures with different structural parameters,and the rationality of the equivalent model was verified, and the frequency transmission curves were obtained. The result shows that the structure is a locally resonant phononic crystal, and there is a wide bandgap in a frequency range of 36.27-246.91 Hz. By changing the structure parameters, we can further widen the bandgap and bring down the bandgap frequency. The vibration attenuation of 121.86 dB can be achieved when the frequency is contained in the gap range for optimizing the structure. The results obtained could provide a reference for the design of phononic crystal structures.
A kind of honeycomb structure phononic crystal was designed, and analyzed by finite element method. Its band structure diagram was calculated, and several vibration modes were analyzed to elucidate the bandgaps mechanism. Equivalent models were established for the vibration modes of the first bandgap and the cut-off frequency, respectively. The effect of structural parameters on the bandgap was investigated though calculating the energy band diagrams of crystal structures with different structural parameters,and the rationality of the equivalent model was verified, and the frequency transmission curves were obtained. The result shows that the structure is a locally resonant phononic crystal, and there is a wide bandgap in a frequency range of 36.27-246.91 Hz. By changing the structure parameters, we can further widen the bandgap and bring down the bandgap frequency. The vibration attenuation of 121.86 dB can be achieved when the frequency is contained in the gap range for optimizing the structure. The results obtained could provide a reference for the design of phononic crystal structures.
引文
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[2]SIGALAS M,ECONOMOU E N.Band structure of elastic waves in two dimensional systems[J].Solid State Commun,1993,86(3):141?143.
[3]KUSHWAHA M S,HALEVI P,DOBRZYNSKI L,et al.Acoustic band structure of periodic elastic composites[J].Phys Rev Lett,1993,71(13):2022?2025.
[4]MARTINEZ-SALA R,SANCHO J,SANCHEZ J V,et al.Sound attenuation by sculpture[J].Nature,1995,378(6554):241?241.
[5]LIU Z,ZHANG X,MAO Y,et al.Locally Resonant Sonic Mater[J].Science,289.
[6]YANG Z,DAI H M,CHAN N H,et al.Acoustic metamaterial panels for sound attenuation in the 50?1000 Hz regime[J].Appl Phys Lett,2010,96(4):041906
[7]XIAO Y,WEN J,WEN X.Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators[J].J Sound Vib,2012,331(25):5408?5423.
[8]ZHANG S W,WU J H.Low-frequency bandgaps in phononic crystals with composite locally resonant structures[J].Acta Phys Sin,2013,62(13):305?313.
[9]JIUHUI W U.Low-frequency vibration characteristics of periodic spiral resonators in phononic crystal plates[J].J Mech Eng,2013,49(10):62?69.
[10]GAO N,WU J H,YU L.Research on bandgaps in two-dimensional phononic crystal with two resonators[J].Ultrasonics,2015,56:287?293.
[11]LI Y,CHEN T,WANG X,et al.Band structures in two-dimensional phononic crystals with periodic Jerusalem cross slot[J].Phys B:Condens Matter,2015,456:261?266.
[12]RIEDINGER R,HONG S,NORTE R A,et al.Non-classical correlations between single photons and phonons from a mechanical oscillator.[J].Nature,2016,530(7590):313?316.
[13]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.J Chin Ceram Soc,2016,44(10):1440?1445.
[14]祁鹏山,杜军,姜久龙,等.二维声子晶体的隔声机理及其特性[J].硅酸盐学报,2016,44(10):1458?1464.QI Pengshan,DU Jun,JIANG Jiulong,et al.J Chin Ceram Soc,2016,44(10):1458?1464.
[15]蒋娟娜,姚宏,赵静波,等.新型多重开孔式声子晶体低频带隙研究[J].压电与声光,2018,40(5):709?714,719.JIANG Juanna,YAO Hong,ZHAO Jingbo,et al.J Piezoelectr Acustoopt(in Chinese),2018,40(5):709?714,719.
[16]张帅,郭书祥,姚宏,等.新型多重谐振结构声子晶体带隙特性研究[J].人工晶体学报,2018,47(1):1?8.ZHANG Shuai,GUO Shuxiang,YAO Hong,et al.J Synth Cryst(in Chinese),2018,47(1):1?8.
[17]温熙森等.声子晶体[M].北京:国防工业出版社,2009:292?293.
[18]ABDELKRIM Khelif,ALi Adibi.声子晶体基本原理与应用[M].舒海生等译.北京:国防工业出版社,2018:75?92.ABDELKRIM Khelif,ALI Adibi.Phononic Crystals:Fundamentals and Application[M].SHU Haisheng,et al.trans.Beijing:National Defense Industry Press,2018:75?92.
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