Locally resonant sonic materials

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Abstract

We have fabricated a new type of composite which displays localized sonic resonances at ∼350–2000Hz with a microstructure size in the millimeter to centimeter range. Around the resonance frequencies the composite behaves as a material with effective negative elastic constants and as a total wave reflector—a 2cm slab of this material is shown to break the conventional mass-law of sound transmission by order(s) of magnitude. When the microstructure is periodic, our composites exhibit large elastic wave band gaps at the sonic frequency range, with a lattice constant order(s) of magnitude smaller than the corresponding sonic wavelength in air. Good agreement is obtained between theory and experiment.

Introduction

In recent years, the study of classical wave characteristics in periodic structures, the so-called spectral band-gap crystals, is an active area of research due to their novel photonic and acoustic characteristics [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. Photonic band-gap crystals, for example, forbid the propagation of electromagnetic waves in certain frequency regimes and hold promise for a host of potential applications such as extremely low threshold lasers. Their existence was first theoretically predicted and then experimentally realized [1], [16], [17], [18], [19]. In contrast, the realization of acoustic wave band-gap crystals is hampered by two difficulties. The first is that at sonic frequencies, the requirement that the lattice constant be comparable to the acoustic wavelength implies an extremely large scale (comparable to large outdoor sculptures) for the required structure, thus putting 3D sonic band-gap crystals essentially out of reach for most laboratories. Second, similar to photonic crystals, the existence of a 3D acoustic/elastic band gap in a two-component composite is predicted to be sensitive to not only the symmetry of the periodic structure, but also to the materials properties.

In this paper, we report a new paradigm for the realization of robust elastic wave band gaps in the sonic frequency range. By considering the idea of localized sonic resonances, we have demonstrated theoretically and experimentally that not only is it possible to realize sonic band-gap crystals with a lattice constant order(s) of magnitude smaller than the acoustic wavelength, but the band gap can also exist for non-periodic structures. These results can lead to practical applications for the sonic band-gap materials, such as effective low-frequency sound shield that breaks the mass density law for sound transmission.

Section snippets

Theoretical background

To explain the basic idea, it is instructive to first introduce the concept of localized resonances, by drawing an analogy with the atomic electronic levels and their effect on optical properties of an atomic gas. Atoms are known to have discrete electronic energy levels. In the Lorentzian formulation of atom–light interaction, an atomic “resonance” occurs when the light frequency (times Planck's constant) coincides with the difference between two electronic energy levels. Since visible light

Experimental

We have realized the structure geometry shown in Fig. 1 by using 1.0cm diameter lead balls coated with 0.25cm of silicon rubber. We have measured two types of samples. The first one is a circular slab 9.8cm in diameter and 2.1cm in thickness. This sample contains 48vol% of randomly dispersed monolayer of the rubberized metallic particles [21]. The second sample is an 8×8×8 simple cubic crystal with a lattice constant of 1.55cm. The matrix is epoxy for both samples. Sonic transmission was

Results and discussion

Fig. 2 shows the measured amplitude transmission (thick solid line) through sample 1. As a reference, the measured amplitude transmission through a 2.1cm slab of epoxy is also plotted (thin solid line). The striking difference in the transmission coefficient between sample 1 and the pure epoxy slab is the existence of two dips centered at 400 and 1100Hz for sample 1. These dips originate from the partially developed spectral gaps caused by negative effective elastic constants. It is also found

Conclusion

Based on simple construction, we have fabricated a novel sonic band-gap material using locally resonant structures. Extension to lower and higher frequency elastic wave systems may lead to applications in seismic wave reflection and ultrasonics.

Acknowledgments

This work is supported in part by the Hong Kong RGC Grant HKUST6145/99P.

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1

Present address: Department of Physics, Wuhan University, Wuhan, China.

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