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We have fabricated sonic crystals, based on the idea of localized resonant structures, that exhibit spectral gaps with a lattice constant two orders of magnitude smaller than the relevant wavelength. Disordered composites made from such localized resonant structures behave as a material with effective negative elastic constants and a total wave reflector within certain tunable sonic frequency ranges. A 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.
Complete sound attenuation for a certain frequency range can be achieved through the concept of a "classical wave spectral gap," originally introduced in relation to the electromagnetic wave, denoted the "photonic band gap" (1). Subsequently extended to elastic waves (2-5), the idea states that a strong periodic modulation in density and/or sound velocity can create spectral gaps that forbid wave propagation. However, the spatial modulation must be of the same order as the wavelength in the gap. It is thus not practical for shielding acoustic sound, because the structure would have to be the size of outdoor sculptures in order to shield environmental noises (5).
We present a class of sonic crystals that exhibit spectral gaps with lattice constants two orders of magnitude smaller than the relevant sonic wavelength. Our materials are based on the simple realization that composites with locally resonant structural units can exhibit effective negative elastic constants at certain frequency ranges. If a wave with angular frequency omega interacts with a medium carrying a localized excitation with frequency omega^sub o^, the linear response functions will be proportional to 1/(omega^sub o^^sup 2^ omega^sup 2^). Such an effect is manifest in the electromagnetic frequency response of materials with optical resonances, where a negative dielectric constant epsilon (generally on the higher frequency side of the resonance) implies a purely imaginary wave vector k = n(omega)/c (where n is the index of refraction and c is the speed of light) and hence exponential attenuation of the electromagnetic wave (6). Here, we implement this idea in the context of elastic composites at sonic frequencies. By varying the size and geometry of the structural unit, we can tune the frequency ranges over which the effective elastic constants are negative.
Our composites...