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动态质量密度和声学超常介质

Dynamic mass density and acoustic metamaterials

  • 摘要: 复合介质的质量密度通常认为是组成它的各种成分的质量密度的体平均值.体平均质量密度常常被用于计算在长波长极限下的声波速度,在此极限下波长比复合介质中的特征尺度要大得多.作者通过严格的数学推导证明,计算(长波长极限下的)波速时所用到的动态质量密度与静态的体平均质量密度有显著的不同.这一发现与最近的实验结果符合得非常好,并且使得声学超常介质的实现成为可能.这两种质量密度之所以不同的物理根源就在于,在波场中复合介质中的各个成分之间有相对的运动.也就是说,隐含的假定——在长波长极限下复合介质中的各个成分必定会全体同相地运动——将不再正确,尤其是当各个成分的声学阻抗之间有较大的差异时.实验和理论显示,对于局域共振声学材料而言,动态质量密度甚至还会变成是负的.文章探讨了这一发现的物理意义,以及它在声学超常介质领域的应用.

     

    Abstract: The mass density of a composite is generally taken as the volume-averaged value of the components′ densities. Moreover, the same volume-averaged mass density is usually used to calculate the wave speed in the long wavelength limit, i.e., where the wavelength is much larger than the size of the inhomogeneities. In this paper we show via rigorous derivation that the dynamic mass density used in the calculation of (long wavelength) wave speed can differ significantly from the static volume averaged value. This recognition is shown to yield an excellent explanation of some recent experimental data, providing a basis for the realization of acoustic metamaterials. The physical reason for the difference between the two mass densities is attributed to the relative motion between the components. That is, the implicit assumption——that all components in a composite must move uniformly in the long wavelength limit——can be violated in the limit of large acoustic impedance contrast between the components. The dynamic mass density can even be negative for the locally resonant sonic materials, as demonstrated both experimentally and theoretically. The implications of this finding, in the context of acoustic metamaterials, are discussed.

     

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