一种圆柱壳类声子晶体振动带隙及振动特性研究
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摘要
圆柱壳类结构在结构设计中应用广泛,其振动噪声问题十分普遍。基于二维板类声子晶体提出了一种基于布拉格散射机理的圆柱壳类声子晶体模型。该模型利用圆柱壳的动力学方程理论和Bloch周期条件,建立其结构有限元模型并分析其振动特性。针对一半径为0.1 m的圆柱壳声子晶体结构,利用有限元法计算能带结构,并分析其振动带隙的特性。为了验证带隙准确性,利用有限元法对多个周期结构圆柱壳模型进行了振动传递分析,获得的振动传递函数曲线与能带带隙相匹配,同时给出了带隙外和带隙内的两个不同频率点的位移场分布。结果表明,与板类结构相似,圆柱壳声子晶体同样具有良好的沿轴线和圆柱环两个方向的带隙或全禁带隙,其振动传递损失也验证该结论。
A cylindrical shell structure is widely used in structure design but its vibration noise problem commonly exists. Based on the theory of two-dimensional plate phononic crystal and the mechanism of Bragg scattering, this work presents a cylindrical shells phononic crystal model. According to the dynamic equation theory of cylindrical shell and Bloch periodic condition, the vibration characteristic of this structure was studied with an established finite element model. This research took a phononic crystal structure with a radius of 0.1 m as an example, calculated its band structure, and analyzed its vibration characteristics. To verify the accuracy of the calculated band gap, the vibration transfer of cylinder shell models with multiple periodic structures was analyzed through the finite element method(FEM). The result shows that the vibration transfer function curve match the band gap well. It indicates that, similar to the plate structure, cylindrical shell phonon crystals also have quite good band gap and total forbidden band gap along the axial line and direction of cylinder ring.
A cylindrical shell structure is widely used in structure design but its vibration noise problem commonly exists. Based on the theory of two-dimensional plate phononic crystal and the mechanism of Bragg scattering, this work presents a cylindrical shells phononic crystal model. According to the dynamic equation theory of cylindrical shell and Bloch periodic condition, the vibration characteristic of this structure was studied with an established finite element model. This research took a phononic crystal structure with a radius of 0.1 m as an example, calculated its band structure, and analyzed its vibration characteristics. To verify the accuracy of the calculated band gap, the vibration transfer of cylinder shell models with multiple periodic structures was analyzed through the finite element method(FEM). The result shows that the vibration transfer function curve match the band gap well. It indicates that, similar to the plate structure, cylindrical shell phonon crystals also have quite good band gap and total forbidden band gap along the axial line and direction of cylinder ring.
引文
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[2]温熙森,温激鸿,郁殿龙,等.声子晶体[M].北京:国防工业出版社,2002.
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[20]郁殿龙,刘耀宗,王刚,等.二维声子晶体薄板的振动特性[J].机械工程学报,2006,42(2):150-154.YU Dianlong,LIU Yaozong,WANG Gang,et al.Vibration property of two dimension phononic crystals thin plate[J].Chinese Journal of Mechanical Engineering,2006,42(2):150-154.
[21]SONG Y,FENG L,WEN J,et al.Analysis and enhancement of flexural wave stop bands in 2D periodic Plates[J].Physics Letters A,2015,379:1449-1456.
[22]DOYLE J F.Wave propagation in structures:spectral analysis using fast discrete fourier transforms[M].New York:Springer-Verlag,1997.
[23]TYUTEKIN V.Helical waves of an elastic cylindrical shell[J].Acoustical Physics,2004,50:273-280.
[24]PANY C,PARTHAN S.Axial wave propagation in long periodic curved panels[J].Journal of Vibration and Acoustics,2003,125:24-30.
[25]MANCONI E,MACE B.Wave characterization of cylindrical and curved panels using a finite element method[J].The Journal of Acoustical Society of America,2009,125(1):154-163.
[26]NATEGHI A,VAN BELLE L,CLAEYS C,et al.Wave propagation in locally resonant cylindrically curved metamaterial panels[J].International Journal of Mechanical Sciences,2017,127:73-90.
[27]谢宇晗,尹剑飞,温激鸿.一种环布动力吸振器的圆柱壳声振控制设计[J].噪声与振动控制,2018,38(增刊1):264-268.XIE Yuhan,YIN Jianfei,WEN Jihong.Design of vibroacoustic control of the cylindrical shell via a dynamic vibration absorber annulus[J].Noise and Vibration Control,2018,38(Sup 1):264-268.
[28]黄昆.固体物理学[M].北京:人民出版社,1979.
[2]温熙森,温激鸿,郁殿龙,等.声子晶体[M].北京:国防工业出版社,2002.
[3]SIGALAS M,ECONOMOU E N.Band structure of elastic waves in two dimensional systems[J].Solid State Commun,1993,86(3):141-143.
[4]KUSHWAHA M S,HALEVI P,MARTINEZ G,et al.Theory of acoustic band structure of periodic elastic composites[J].Physical Review B Condensed Matter,1994,49(4):2313-2322.
[5]WANG G,WEN X,WEN J,et al.Two-dimensional locally resonant phononic crystals with binary structures[J].Physical Review Letters,2004,93(15):154302.
[6]WU T T,HSU J C,SUN J H.Phononic plate waves[J].Ultrasonics Symposium,2011,58(10):2146-2161.
[7]LEE G Y,CHONG C,KEVREKIDIS P G,et al.Wave mixing in coupled phononic crystals via a variable stiffness mechanism[J].Journal of the Mechanics and Physics of Solids,2016,95:501-516.
[8]LIU Z,ZHANG X,MAO Y,et al.Locally resonant sonic materials[J].Science,2000,289(5485):1734-17366.
[9]温激鸿.声子晶体振动带隙及减振特性研究[D].长沙:国防科技大学,2005.
[10]LIU Z,CHAN C T,SHENG P.Three-component elastic wave band-gap material[J].Physical Review B Condensed Matter,2002,65(16):165116.
[11]ZHANG X,LIU Y,WU F,et al.Large two-dimensional band gaps in three component phononic crystals[J].Physics Letters A,2003,317(1):144-149.
[12]冯端,金国均.凝聚态物理学[M].北京:高等教育出版社,2013.
[13]JENSEN J.Phononic band gaps and vibrations in one-and two-dimensional mass-spring structures[J].Journal of Sound&Vibration,2003,266(5):1053-1078.
[14]SONG Y,WEN J,YU D,et al.Reduction of vibration and noise radiation of an underwater vehicle due to propeller forces using periodically layered isolators[J].Journal of Sound and Vibration,2014,333(14):3031-3043.
[15]SHARMA B,SUN C T.Impact load mitigation in sandwich beams using local resonators[J].Journal of Sandwich Structures&Materials,2016,18:50-64.
[16]赵浩江,宋扬,刘荣强.轮辐板式局域共振声子晶体隔振器的振动特性研究[J].振动与冲击,2017,36(15):43-50.ZHAO Haojiang,SONG Yang,LIU Rongqiang.Vibration characteristics of spoke-like vibration isolators with locally resonant photonic crystal plates[J].Journal of Vibration and Shock,2017,36(15):43-50.
[17]HE Z C,XIAO X,LI E.Design for structural vibration suppression in laminate acoustic metamaterials[J].Composites Part B:Engineering,2017,131:237-252.
[18]温激鸿,郁殿龙,王刚,等.周期结构细直梁弯曲振动中的振动带隙[J].机械工程学报,2005,41(4):1-6.WEN Jihong,YU Dianlong,WANG Gang,et al.Elastic wave band gaps in flexural vibrations of straight beams[J].Chinese Journal of Mechanical Engineering,2005,41(4):1-6.
[19]WANG M Y,WANG X.Frequency band structure of locally resonant periodic flexural beams suspended with force-moment resonators[J].Journal of Physics D:Applied Physics,2013,46(46):255502.
[20]郁殿龙,刘耀宗,王刚,等.二维声子晶体薄板的振动特性[J].机械工程学报,2006,42(2):150-154.YU Dianlong,LIU Yaozong,WANG Gang,et al.Vibration property of two dimension phononic crystals thin plate[J].Chinese Journal of Mechanical Engineering,2006,42(2):150-154.
[21]SONG Y,FENG L,WEN J,et al.Analysis and enhancement of flexural wave stop bands in 2D periodic Plates[J].Physics Letters A,2015,379:1449-1456.
[22]DOYLE J F.Wave propagation in structures:spectral analysis using fast discrete fourier transforms[M].New York:Springer-Verlag,1997.
[23]TYUTEKIN V.Helical waves of an elastic cylindrical shell[J].Acoustical Physics,2004,50:273-280.
[24]PANY C,PARTHAN S.Axial wave propagation in long periodic curved panels[J].Journal of Vibration and Acoustics,2003,125:24-30.
[25]MANCONI E,MACE B.Wave characterization of cylindrical and curved panels using a finite element method[J].The Journal of Acoustical Society of America,2009,125(1):154-163.
[26]NATEGHI A,VAN BELLE L,CLAEYS C,et al.Wave propagation in locally resonant cylindrically curved metamaterial panels[J].International Journal of Mechanical Sciences,2017,127:73-90.
[27]谢宇晗,尹剑飞,温激鸿.一种环布动力吸振器的圆柱壳声振控制设计[J].噪声与振动控制,2018,38(增刊1):264-268.XIE Yuhan,YIN Jianfei,WEN Jihong.Design of vibroacoustic control of the cylindrical shell via a dynamic vibration absorber annulus[J].Noise and Vibration Control,2018,38(Sup 1):264-268.
[28]黄昆.固体物理学[M].北京:人民出版社,1979.