Functionally graded metamaterial for broadband sound isolation

What is it about?

Our analysis shows, for their first time, that a functionally graded mechanical metamaterial can highly attenuate sound and vibration propagation over a frequency band that extends from an arbitrarily low threshold all the way to, theoretically, infinity. A method based on the concept of Fourier transfer and backward substitution was developed to more easily compute the transmittance spectrum of 1D metamaterials based on spring-mass resonator chains with a finite number of units, and then used to conduct a parametric study of chains with linear variations of masses and spring stiffnesses. The key result is that with proper tuning of the gradient parameters the upper limit of the low-transmittance band can be extended up to infinity, at least in theory. In reality, there is an upper limit where the long- wavelength assumption underpinning the lumped mass and stiffness chain model is no longer valid. It is important to note that systems with nine or ten units were sufficient to achieve broadband behaviour and performance changes relatively little for longer chains.

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Why is it important?

Metamaterials can provide exotic behaviours and unique properties not previously available from conventional materials, and can be used to manipulate wave propagation in new and counterintuitive ways. In practice they often exploit resonance phenomena to generate these unusual properties, which greatly limits their bandwidth. For applications such as sound and vibration isolation, electromagnetic and acoustic cloaking, among others, a wide bandwidth considerably broadens the potential usefulness of metamaterials. More broadly, one-dimensional chains of coupled spring-mass oscillators are suitable for modelling several physical systems arising from various scientific areas, such as condensed matter physics, optics, chemistry, acoustics and mechanics. In all these areas, a uniformly periodic arrangement of identical linear resonating units is normally used which limits their effectiveness to a narrow frequency range. The most important finding is that varying the spring stiffnesses along the resonator chain can create a resonant frequency gradient and can be tailored to broaden the effective metamaterial bandwidth in ways that are impossible to achieve by just optimizing the characteristics of uniformly periodic 1D metamaterials. This analysis also indicates that frequency graded metamaterials provide an avenue towards additional dimensions of control over band structures. While experimental verification and further research on the effect of other gradient types are needed, this is a significant step forward in the development of practical designs for wideband resonant metamaterials.