十字型结构声子晶体带隙及等效模型研究
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摘要
该文设计了一种新型十字型声子晶体结构,并采用有限元法对其进行了研究;分析了此结构若干共振频率下的振动模态,分别建立了带隙起始频率与截止频率处振动模态的简化模型,探究了结构与材料参数对带隙的影响,验证了简化模型的合理性;最后计算了结构的反射系数与透射系数。结果表明,该结构带隙产生机理属局域共振型,能够在中低频段内产生一个完全带隙。通过对金属芯体密度、基体密度、包覆层的宽度及弹性模量等因素的调节,可以实现对带隙上、下界频率的调节,结构的反射系数与透射系数随入射波频率的变化也与带隙图相应证,当带隙图显示出现带隙时,结构的透射系数也随之下降。
A novel cross-shaped phononic crystal structure is designed and studied by using the finite element method in this paper.Meanwhile,the vibration modalities of this structure at several resonant frequencies are analyzed,the simplified model of the vibration modalities at the starting frequency and the cut-off frequency of the band gap is established,the effect of structure and material parameters on the band gap is explored,and the rationality of the simplified model is verified.Finally,the reflection coefficient and transmission coefficient of the structure are calculated.The results show that the band gap generation mechanism of the structure belongs to local resonance type.It can produce a complete band gap in the middle and low frequency segments.By adjusting the density of metal core and matrix,the width and the modulus elasticity of the coating,the adjustment of the frequency of the upper and lower bounds of the band gap can be realized.The reflection and transmission coefficients of the crystal structure vary with the frequency of the incident wave,which corresponds to the band gap diagram.When the band gap diagram shows a band gap,the transmission coefficient of the structure also decreases.
A novel cross-shaped phononic crystal structure is designed and studied by using the finite element method in this paper.Meanwhile,the vibration modalities of this structure at several resonant frequencies are analyzed,the simplified model of the vibration modalities at the starting frequency and the cut-off frequency of the band gap is established,the effect of structure and material parameters on the band gap is explored,and the rationality of the simplified model is verified.Finally,the reflection coefficient and transmission coefficient of the structure are calculated.The results show that the band gap generation mechanism of the structure belongs to local resonance type.It can produce a complete band gap in the middle and low frequency segments.By adjusting the density of metal core and matrix,the width and the modulus elasticity of the coating,the adjustment of the frequency of the upper and lower bounds of the band gap can be realized.The reflection and transmission coefficients of the crystal structure vary with the frequency of the incident wave,which corresponds to the band gap diagram.When the band gap diagram shows a band gap,the transmission coefficient of the structure also decreases.
引文
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[18]MATLACK K H,BAUHOFER A,KRDEL S,et al.Composite 3D-printed metastructures for low-frequency and broadband vibration absorption[J].Proceedings of the National Academy of Sciences of the United States of America,2016,113(30):8386.
[19]DAI H,LIU T,JIAO J,et al.Double Dirac cone in twodimensional phononic crystals beyond circular cells[J].Journal of Applied Physics,2017,121(13):135105.
[2]KUSHWAHA M S,HALEVI P,DOBRZYNSKI L,et al.Acoustic band structure of periodic elastic composites[J].International Journal of Modern Physics B,1993,10(9):9600039.
[3]MARTINEZSALA R,SANCHO J,SANCHEZ J V,et al.Sound attenuation by sculpture[J].Nature,1995,378(6554):241-241.
[4]LIU Z,ZHANG X,MAO Y,et al.Locally resonant sonic materials[J].Science,2000,289(5485):1734.
[5]KIN M H,CHUN K C,YANG Z,et al.Broadband locally resonant sonic shields[J].Appl Phys Lett,2003,83(26):5566-5568.
[6]LI J,CHAN C T.Double-negative acoustic metamaterial[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2004,70(5):055602.
[7]YANG Z,DAI H M,CHAN N H,et al.Acoustic metamatrril panels for sound attenuation in the 50-1 000Hz regime[J].Applied Physics Letters,2010,96(4):1833.
[8]MEI J,MA G,YANG M,et al.Dark acoustic metamaterials as super absorbers for low-frequency sound[J].Nat Commun,2012,3:756-762.
[9]LAI Y,WU Y,SHENG P,et al.Hybrid elastic solids[J].Nat Mater,2011,10(8):620-624.
[10]温激鸿,王刚,郁殿龙,等.声子晶体振动带隙及减振特性研究[J].中国科学,2007,37(9):1126-1139.
[11]YANG Z,DAI H M,CHAN N H,et al.Acoustic metamaterial panels for sound attenuation in the 50-1000Hz regime[J].Applied Physics Letters,2010,96(4):1833.
[12]XIAO Y,WEN J,WEN X.Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators[J].Journal of Sound&Vibration,2012,331(25):5408-5423.
[13]ZHANG S W,WU J H.Low-frequency band gaps in phononic crystals with composite locally resonant structures[J].Acta Physica Sinica,2013,62(13):134302.
[14]JIUHUI W U.Low-frequency vibration characteristics of periodic spiral resonators in phononic crystal plates[J].Journal of Mechanical Engineering,2013,49(10):62.
[15]GAO N,WU J H,YU L.Research on bandgaps in twodimensional phononic crystal with two resonators[J].Ultrasonics,2015,56:287-293.
[16]LI Y,CHEN T,WANG X,et al.Band structures in two-dimensional phononic crystals with periodic Jerusalem cross slot[J].Physica B Condensed Matter,2015,456:261-266.
[17]RIEDINGER R,HONG S,NORTE R A,et al.Nonclassical correlations between single photons and phonons from a mechanical oscillator[J].Nature,2016,530(7590):313.
[18]MATLACK K H,BAUHOFER A,KRDEL S,et al.Composite 3D-printed metastructures for low-frequency and broadband vibration absorption[J].Proceedings of the National Academy of Sciences of the United States of America,2016,113(30):8386.
[19]DAI H,LIU T,JIAO J,et al.Double Dirac cone in twodimensional phononic crystals beyond circular cells[J].Journal of Applied Physics,2017,121(13):135105.