周期新型超材料板多阶弯曲波带隙研究
|
摘要
利用了声子晶体带隙性质的概念,结合局域共振原理,提出了一种新型周期超材料板结构。这种结构是由具有负等效模量的声学超材料子结构作为共振单元,周期排列在薄板上形成的。在共振单元的作用下,不仅在低频范围内产生带阻特性,还引起了部分弯曲波发生波型转换并产生相应的多阶带隙,使得在多个频段范围内阻断波的传播,扩大了抑制振动传递的频率范围。利用平面波展开方法分析了结构的弯曲波带隙,并且和有限元方法得到结果进行比较,得到了一致的频散关系。对有限超材料板的振动传递损失也进行了分析,数值计算结果证明了所求频散关系的正确性以及本文提出的隔振结构对振动衰减的有效性。除此之外,研究了局域共振单元的参数和单胞尺寸对结构带隙性质产生的影响,为选取合适的参数满足特定隔振要求(低频,宽带等)的超材料板结构提供了参考依据。
A new periodic metamaterial plate was proposed based on the concept of the phononic crystal and local resonance mechanism. The proposed structure consists of negative modulus acoustic metamaterial microstructures acting as local resonators. The structure not only exhibits low frequency stop band characteristics,but also provides multi-flexural band gaps,and leads to the transformation of partially flexural waves. Since no wave energy propagation is allowable in the multi-frequency domain,the frequency domain for vibration transmission mitigation in the structure is broadened. The dispersion relation was acquired by using the plane wave expansion method. A comparison between the results obtained by the plane wave expansion and finite element method was presented and a good correspondence between the results of both methods was found. The vibration transmission loss of a finite metamaterial plate was calculated to validate the band gap,demonstrating the efficiency of the vibration isolation. Moreover,a parametric study was implemented to investigate the effects of parameters of the local resonators and unit cell on the band gap property,which makes it possible to satisfy the specific requirements( low frequency,wide band gap,etc) of metamaterial plates for vibration isolation.
A new periodic metamaterial plate was proposed based on the concept of the phononic crystal and local resonance mechanism. The proposed structure consists of negative modulus acoustic metamaterial microstructures acting as local resonators. The structure not only exhibits low frequency stop band characteristics,but also provides multi-flexural band gaps,and leads to the transformation of partially flexural waves. Since no wave energy propagation is allowable in the multi-frequency domain,the frequency domain for vibration transmission mitigation in the structure is broadened. The dispersion relation was acquired by using the plane wave expansion method. A comparison between the results obtained by the plane wave expansion and finite element method was presented and a good correspondence between the results of both methods was found. The vibration transmission loss of a finite metamaterial plate was calculated to validate the band gap,demonstrating the efficiency of the vibration isolation. Moreover,a parametric study was implemented to investigate the effects of parameters of the local resonators and unit cell on the band gap property,which makes it possible to satisfy the specific requirements( low frequency,wide band gap,etc) of metamaterial plates for vibration isolation.
引文
[1]SHENG P,ZHANG X X,LIU Z,et al.Locally resonant sonic materials[J].Science,2003,338(1/2/3/4):201-205.
[2]WANG Y F,WANG Y S.Complete bandgaps in twodimensional phononic crystal slabs with resonators[J].Journal of Applied Physics,2013,114(4):1-15.
[3]ROMERO-GARCA V,KRYNKIN A,GARCIA-RAFFI L M,et al.Multi-resonant scatterers in sonic crystals:locally multi-resonant acoustic metamaterial[J].Journal of Sound and Vibration,2013,332(1):184-198.
[4]WANG Y F,WANG Y S,ZHANG C.Bandgaps and directional propagation of elastic waves in 2 D square zigzag lattice structures[J].Journal of Physics D Applied Physics,2014,47(48):485102.
[5]LIU Y,YU D,LI L,et al.Design guidelines for flexural wave attenuation of slender beams with local resonators[J].Physics Letters A,2007,362(5/6):344-347.
[6]XIAO Y,WEN J,WEN X.Flexural wave band gaps in locally resonant thin plates with periodically attached springmass resonators[J].Journal of Physics D Applied Physics,2012,45(19):195401-195412.
[7]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 and Vibration,2012,331(25):5408-5423.
[8]ZHANG H,XIAO Y,WEN J,et al.Flexural wave band gaps in metamaterial beams with membrane-type resonators:theory and experiment[J].Journal of Physics D Applied Physics,2015,48(43):435305.
[9]SONG Y,FENG L,WEN J,et al.Reduction of the sound transmission of a periodic sandwich plate using the stop band concept[J].Composite Structures,2015,128:428-436.
[10]SHARMA B,SUN C T.Local resonance and Bragg bandgaps in sandwich beams containing periodically inserted resonators[J].Journal of Sound and Vibration,2016,364:133-146.
[11]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.
[12]郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究[D].长沙:国防科学技术大学,2006.
[13]郁殿龙,温激鸿,陈圣兵,等.轴向载荷周期结构梁的弯曲振动带隙特性[J].振动与冲击,2010,29(3):85-88.YU Dianlong,WEN Jihong,CHEN Shengbing,et al.Flexural vibration band gaps in axially loaded periodic beam structure[J].Journal of Vibration and Shock,2010,29(3):85-88.
[14]陈荣,吴天行.周期结构空腹梁的动态特性研究[J].振动与冲击,2013,32(14):122-126.CHEN Rong,WU Tianxing.Dynamic characteristics of a periodic hollow beam[J].Journal of Vibration and Shock,2013,32(14):122-126.
[15]舒海生,张法,刘少刚,等.一种特殊的布拉格型声子晶体杆振动带隙研究[J].振动与冲击,2014,33(19):147-151.SHU Haisheng,ZHANG Fa,LIU Shaogang,et al.Vibration band gap of a special rod of phononic crystals[J].Journal of Vibration and Shock,2014,33(19):147-151.
[16]孙勇敢,黎胜.周期性加肋板振动带隙研究[J].船舶力学,2016,20(增刊1):142-147.SUN Yonggan,LI Sheng.Vibration band gap research of periodic stiffened plates[J].Journal of Ship Mechanics,2016,20(Sup1):142-147.
[17]HUANG H H,SUN C T.Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young's modulus[J].Journal of the Mechanics and Physics of Solids,2011,59(10):2070-2081.
[18]WANG T,SHENG M P,QIN Q H.Multi-flexural band gaps in an Euler-Bernoulli beam with lateral local resonators[J].Physics Letters A,2016,380(4):525-529.
[19]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):55401-55409.
[20]GOFFAUX C,SNCHEZ-DEHESA J,YEYATI A L,et al.Evidence of Fano-Like interference phenomena in locally resonant materials[J].Physical Review Letters,2002,88(22):1-53.
[21]XIAO Y,MACE B R,WEN J,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.
[22]XIAO Y,WEN J,YU D,et al.Flexural wave propagation in beams with periodically attached vibration absorbers:Bandgap behavior and band formation mechanisms[J].Journal of Sound and Vibration,2013,332(4):867-893.
[2]WANG Y F,WANG Y S.Complete bandgaps in twodimensional phononic crystal slabs with resonators[J].Journal of Applied Physics,2013,114(4):1-15.
[3]ROMERO-GARCA V,KRYNKIN A,GARCIA-RAFFI L M,et al.Multi-resonant scatterers in sonic crystals:locally multi-resonant acoustic metamaterial[J].Journal of Sound and Vibration,2013,332(1):184-198.
[4]WANG Y F,WANG Y S,ZHANG C.Bandgaps and directional propagation of elastic waves in 2 D square zigzag lattice structures[J].Journal of Physics D Applied Physics,2014,47(48):485102.
[5]LIU Y,YU D,LI L,et al.Design guidelines for flexural wave attenuation of slender beams with local resonators[J].Physics Letters A,2007,362(5/6):344-347.
[6]XIAO Y,WEN J,WEN X.Flexural wave band gaps in locally resonant thin plates with periodically attached springmass resonators[J].Journal of Physics D Applied Physics,2012,45(19):195401-195412.
[7]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 and Vibration,2012,331(25):5408-5423.
[8]ZHANG H,XIAO Y,WEN J,et al.Flexural wave band gaps in metamaterial beams with membrane-type resonators:theory and experiment[J].Journal of Physics D Applied Physics,2015,48(43):435305.
[9]SONG Y,FENG L,WEN J,et al.Reduction of the sound transmission of a periodic sandwich plate using the stop band concept[J].Composite Structures,2015,128:428-436.
[10]SHARMA B,SUN C T.Local resonance and Bragg bandgaps in sandwich beams containing periodically inserted resonators[J].Journal of Sound and Vibration,2016,364:133-146.
[11]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.
[12]郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究[D].长沙:国防科学技术大学,2006.
[13]郁殿龙,温激鸿,陈圣兵,等.轴向载荷周期结构梁的弯曲振动带隙特性[J].振动与冲击,2010,29(3):85-88.YU Dianlong,WEN Jihong,CHEN Shengbing,et al.Flexural vibration band gaps in axially loaded periodic beam structure[J].Journal of Vibration and Shock,2010,29(3):85-88.
[14]陈荣,吴天行.周期结构空腹梁的动态特性研究[J].振动与冲击,2013,32(14):122-126.CHEN Rong,WU Tianxing.Dynamic characteristics of a periodic hollow beam[J].Journal of Vibration and Shock,2013,32(14):122-126.
[15]舒海生,张法,刘少刚,等.一种特殊的布拉格型声子晶体杆振动带隙研究[J].振动与冲击,2014,33(19):147-151.SHU Haisheng,ZHANG Fa,LIU Shaogang,et al.Vibration band gap of a special rod of phononic crystals[J].Journal of Vibration and Shock,2014,33(19):147-151.
[16]孙勇敢,黎胜.周期性加肋板振动带隙研究[J].船舶力学,2016,20(增刊1):142-147.SUN Yonggan,LI Sheng.Vibration band gap research of periodic stiffened plates[J].Journal of Ship Mechanics,2016,20(Sup1):142-147.
[17]HUANG H H,SUN C T.Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young's modulus[J].Journal of the Mechanics and Physics of Solids,2011,59(10):2070-2081.
[18]WANG T,SHENG M P,QIN Q H.Multi-flexural band gaps in an Euler-Bernoulli beam with lateral local resonators[J].Physics Letters A,2016,380(4):525-529.
[19]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):55401-55409.
[20]GOFFAUX C,SNCHEZ-DEHESA J,YEYATI A L,et al.Evidence of Fano-Like interference phenomena in locally resonant materials[J].Physical Review Letters,2002,88(22):1-53.
[21]XIAO Y,MACE B R,WEN J,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.
[22]XIAO Y,WEN J,YU D,et al.Flexural wave propagation in beams with periodically attached vibration absorbers:Bandgap behavior and band formation mechanisms[J].Journal of Sound and Vibration,2013,332(4):867-893.