双局域共振Helmholtz声子晶体带隙研究
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摘要
设计了一种双局域共振原理的Helmholtz型声子晶体结构,该结构采用U字型嵌套设计,分为内外两个腔,摆脱了内腔空气对带隙上限的影响,使得低频带隙上限得以大大提高。在分析低频带隙形成机理和影响因素时,将弹性杆-弹簧模型引入理论计算,使得简化模型计算精度得以提高。研究表明:该结构具有良好的低频带隙特性,其最低带隙范围为86. 9～445. 9 Hz。结构低频带隙主要受晶格常数、壁厚、细管宽度和长度的影响。在保持其它参数不变的情况下,带隙上限随晶格常数、壁厚和细管长度的增加而降低,随细管宽度的增加而增加;带隙下限随晶格常数、细管长度的增加而降低,随细管宽度、壁厚的增大而增大。该研究为低频噪声控制提供了一定的理论支持,拓宽了声子晶体的设计思路。
A Helmholtz type sonic crystal structure with double local resonance is designed. This structure adopts u-shaped nested design and is divided into inner and outer cavities,which gets rid of the influence of inner cavity air on the upper limit of bandgap and greatly increases the upper limit of low-frequency bandgap. When the low frequency band gap forming mechanism and influencing factors are analyzed,the elastic bar-spring model is introduced into the theoretical calculation,so that the calculation accuracy of the simplified model can be improved. The results show that the structure has good low-frequency band gap characteristics,and its minimum band gap is 86. 9-445. 9 Hz. The low frequency band gap of the structure is mainly affected by lattice constant,wall thickness,width and length of thin tube. With other parameters unchanged,the upper limit of the band gap decreases with the increase of lattice constant,wall thickness and length of the tube,and increases with the increase of width of the tube. The lower limit of band gap decreases with the increase of lattice constant and length of thin tube,and increases with the increase of width and thickness of thin tube. This study provides theoretical support for low frequency noise control and broadens the design idea of phononic crystal.
A Helmholtz type sonic crystal structure with double local resonance is designed. This structure adopts u-shaped nested design and is divided into inner and outer cavities,which gets rid of the influence of inner cavity air on the upper limit of bandgap and greatly increases the upper limit of low-frequency bandgap. When the low frequency band gap forming mechanism and influencing factors are analyzed,the elastic bar-spring model is introduced into the theoretical calculation,so that the calculation accuracy of the simplified model can be improved. The results show that the structure has good low-frequency band gap characteristics,and its minimum band gap is 86. 9-445. 9 Hz. The low frequency band gap of the structure is mainly affected by lattice constant,wall thickness,width and length of thin tube. With other parameters unchanged,the upper limit of the band gap decreases with the increase of lattice constant,wall thickness and length of the tube,and increases with the increase of width of the tube. The lower limit of band gap decreases with the increase of lattice constant and length of thin tube,and increases with the increase of width and thickness of thin tube. This study provides theoretical support for low frequency noise control and broadens the design idea of phononic crystal.
引文
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[2] Kushwaha M S,Halevi P,Dobrzynski L,et al. Acoustic Band Structure of Periodic Elastic Composites[J]. Physical Review Letters,1993,71(13):2022.
[3] Liu Z,Zhang X,Mao Y,et al. Locally Resonant Sonic Materials[J]. Physica B Physics of Condensed Matter,2000,289(5485):1734-1736.
[4]董亚科,杜军,姚宏,等.双包覆层局域共振型声子晶体带隙特性研究[J].人工晶体学报,2015,44(12):3676-3680.
[5] Hu X,Chan C T,Zi J. Two-dimensional Sonic Crystals with Helmholtz Resonators[J]. Physical Review E Statistical Nonlinear&Soft Matter Physics,2005,71(5 Pt 2):055601.
[6]包凯,陈天宁,王小鹏,等.嵌套型开缝圆管声子晶体的带隙影响因素研究[J].西安交通大学学报,2016,50(4):124-130.
[7] Jiang J,Yao H,Du J,et al. Multi-cavity Locally Resonant Structure with the Low Frequency and Broad Band-gaps[J]. Aip Advances,2016,6(11):3224-3226.
[8]张建超,杨绍普,郝如江,等.弹性波传播到声发射传感器的声压透射系数研究[J].振动与冲击,2018,37(12):153-158.
[9]杜功焕,朱哲民,龚秀芬.声学基础[M].南京:南京大学出版社,2012.
[10]倪振华.振动力学[M].西安:西安交通大学出版社,1989.