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摘要

针对低频噪声的隔离问题, 设计了一种薄膜底面Helmholtz腔声学超材料, 该超材料由薄膜底面Helmholtz腔附加质量单元构成. 使用有限元法, 计算了超材料在20—1200 Hz频段内的传输损失曲线与各阶共振频率, 并在实验中验证了数值计算的真实性. 研究结果表明, 超材料在20—1200 Hz频段内隔声性能良好, 出现了6个隔声峰, 其中100 Hz以下的2个隔声峰传输损失分别高达44.29 dB与67.43 dB, 整个频段内的最高传递损失为90.18 dB. 相较于单一的Helmholtz腔、薄膜声学超材料或传统材料, 本超材料的隔声性能有了较大提升. 结合共振频率与隔声峰处的振动模式图, 进一步分析了超材料的隔声机理. 计算了超材料的透射系数与反射系数, 使用等效参数提取法, 得到了超材料的等效模量与等效密度, 在隔声峰处发现了负等效密度, 同时发现其等效模量接近于零, 并由能量角度进一步分析了异常等效参数的产生机理. 通过等效电路法, 得到了超材料的声阻抗, 较精确地计算了超材料的首阶共振频率, 并分析了产生误差的原因. 研究了附加偏心质量单元对超材料隔声性能的影响, 发现附加偏心质量单元可以抑制反对称共振模态的出现, 同时大大增加了超材料的隔声峰数量, 在实验中这一说法得以验证.

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Abstract

Aiming at the isolation of low-frequency noise, an acoustic metamaterial is designed based on Helmholtz cavity and thin film structure. It consists of a Helmholtz cavity with film bottom and the mass block attached to the cavity. By the finite element method, the transmission losses and resonance frequencies of metamaterials in a frequency range of 20－1200 Hz are calculated and also verified experimentally. The results show that the metamaterial has great sound insulation performance in the frequency range. There are six sound insulation peaks, of which the two sound insulation peaks below 100 Hz have the transmission losses of 44.29 dB and 67.43 dB, respectively. The maximum transmission loss in the whole frequency range is 90.18 dB. Comparing with the normal Helmholtz cavity or thin film acoustic metamaterial or traditional material, the sound insulation performance of the metamaterial is improved greatly. By analyzing the resonance and vibration mode diagram at the sound insulation peaks comprehensively, the sound insulation mechanism of the metamaterial is further explored. The results show that many resonance modes have no effect on transmission loss only when the resonance mode can be coupled with the incident wave and is not an antisymmetric mode which can affect the transmission loss. The transmission and reflection coefficient of the metamaterial are calculated by the finite element method, and through the method for retrieving effective properties, the effective mass density and effective modulus are obtained. It is found that there is a negative effective mass density at the sound insulation peak, meanwhile the effective modulus is close to zero. The generation mechanism of abnormal equivalent parameters is analyzed from the energy view point. The acoustic impedance of the metamaterial is obtained by an equivalent circuit method, through which the first resonance frequency is calculated relatively accurately. According to the results of the previous study on sound insulation mechanism, the effect of the eccentric mass unit on the sound insulation performance of metamaterial is studied. It is found that the eccentric mass can greatly reduce the antisymmetric resonance mode and increase the sound insulation peak of the structure, which is also verified experimentally. The results provide a reference for designing the acoustic metamaterials.

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作者及机构信息

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通信作者:赵静波,chjzjb@163.com

基金项目:国家自然科学基金(批准号: 11504429)和空军工程大学基础部预研项目(批准号: YNJC119070602)资助的课题

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Corresponding author:Zhao Jing-Bo,chjzjb@163.com

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 11504429) and the Pre-research Project of Department of Basic Sciences, Air Force Engineering University, China (Grant No. YNJC19070602)

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施引文献

下载: 全尺寸图片幻灯片

Material	ρ/kg·m^–3	E/10¹⁰Pa	Possion rate
Tungsten	19100	35.41	0.35
Silastic	1300	1.175 × 10^–5	0.469
Steel	7780	21.06	0.3

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