ABSTRACT
The giant monopole resonance is a well-known phenomenon, employed to tune the dynamic response of composite materials comprising voids in an elastic matrix which has a bulk modulus much greater than its shear modulus, e.g. elastomers. This low frequency resonance (e.g. λ p / a ≈ 100 for standard elastomers, where λ p and a are the compressional wavelength and void radius, respectively) has motivated acoustic material design over many decades, exploiting the subwavelength regime. Despite this widespread use, the manner by which the resonance arising from voids in close proximity is affected by their interaction is not understood. Here, we illustrate that for planar elastodynamics (circular cylindrical voids), coupling due to near-field shear significantly modifies the monopole (compressional) resonant response. We show that by modifying the number and configuration of voids in a metacluster, the directionality, scattering amplitude and resonant frequency can be tailored and tuned. Perhaps most notably, metaclusters deliver a lower frequency resonance than a single void. For example, two touching voids deliver a reduction in resonant frequency of almost 16% compared with a single void of the same volume. Combined with other resonators, such metaclusters can be used as meta-atoms in the design of elastic materials with exotic dynamic material properties.
ABSTRACT
Recent work in the acoustic metamaterial literature has focused on the design of metasurfaces that are capable of absorbing sound almost perfectly in narrow frequency ranges by coupling resonant effects to visco-thermal damping within their microstructure. Understanding acoustic attenuation mechanisms in narrow, viscous-fluid-filled channels is of fundamental importance in such applications. Motivated by recent work on acoustic propagation in narrow, air-filled channels, a theoretical framework is presented that demonstrates the controlling mechanisms of acoustic propagation in arbitrary Newtonian fluids, focusing on attenuation in air and water. For rigid-walled channels, whose widths are on the order of Stokes's boundary layer thickness, attenuation in air at 10 kHz can be over 200 dB m-1; in water it is less than 37 dB m-1. However, in water, fluid-structure-interaction effects can increase attenuation dramatically to over 77 dB m-1 for a steel-walled channel, with a reduction in phase-speed approaching 70%. For rigid-walled channels, approximate analytical expressions for dispersion relations are presented that are in close agreement with exact solutions over a broad range of frequencies, revealing explicitly the relationship between complex phase-speed, frequency and channel width.
