Christopher N. Layman

Highly anisotropic elements for acoustic pentamode applications.

Pentamode metamaterials are a class of acoustic metafluids that are characterized by a divergence free modified stress tensor. Such materials have an unconventional anisotropic stiffness and isotropic mass density, which allow themselves to mimic other fluid domains. Here we present a pentamode design formed by an oblique honeycomb lattice and producing customizable anisotropic properties. It is shown that anisotropy in the stiffness can exceed 3 orders of magnitude, and that it can be realistically tailored for transformation acoustic applications.

Thin Fresnel zone plate lenses for focusing underwater sound

A Fresnel zone plate (FZP) lens of the Soret type creates a focus by constructive interference of waves diffracted through open annular zones in an opaque screen. For underwater sound below MHz frequencies, a large FZP that blocks sound using high-impedance, dense materials would have practical disadvantages. We experimentally and numerically investigate an alternative approach of creating a FZP with thin (0.4λ) acoustically opaque zones made of soft silicone rubber foam attached to a thin (0.1λ) transparent rubber substrate. An ultra-thin (0.0068λ) FZP that achieves higher gain is also proposed and simulated which uses low-volume fraction, bubble-like resonant air ring cavities to construct opaque zones. Laboratory measurements at 200 kHz indicate that the rubber foam can be accurately modeled as a lossy fluid with an acoustic impedance approximately 1/10 that of water. Measured focal gains up to 20 dB agree with theoretical predictions for normal and oblique incidence. The measured focal radius of 0.68λ (peak-to-null) agrees with the Rayleigh diffraction limit prediction of 0.61 λ/NA (NA = 0.88) for a low-aberration lens.

Underwater acoustic omnidirectional absorber

Gradient index media, which are designed by varying local element properties in given geometry, have been utilized to manipulate acoustic waves for a variety of devices. This study presents a cylindrical, two-dimensional acoustic “black hole” design that functions as an omnidirectional absorber for underwater applications. The design features a metamaterial shell that focuses acoustic energy into the shells core. Multiple scattering theory was used to design layers of rubber cylinders with varying filling fractions to produce a linearly graded sound speed profile through the structure. Measured pressure intensity agreed with predicted results over a range of frequencies within the homogenization limit.

Experimental realization of a variable index transmission line metamaterial as an acoustic leaky-wave antenna

Development and experimental realization of an acoustic leaky wave antenna are presented. The antenna uses a one-dimensional composite right/left hand transmission line approach to tune radiation angle continually from backfire-to-endfire, including broadside, as a function of input frequency. An array of acoustically loaded membranes and open channels form a structure with negative, zero, or positive refractive index, depending on excitation frequency. The fast-wave radiation band of the antenna is determined using acoustic circuit analysis. Based on the designs specified by circuit and finite element analysis, an acoustic leaky wave antenna was fabricated, and the radiation direction measured at discrete frequencies.

Experimental Demonstration of Underwater Acoustic Scattering Cancellation.

We explore an acoustic scattering cancellation shell for buoyant hollow cylinders submersed in a water background. A thin, low-shear, elastic coating is used to cancel the monopole scattering from an air-filled, neutrally buoyant steel shell for all frequencies where the wavelength is larger than the object diameter. By design, the uncoated shell also has an effective density close to the aqueous background, independently canceling its dipole scattering. Due to the significantly reduced monopole and dipole scattering, the compliant coating results in a hollow cylindrical inclusion that is simultaneously impedance and sound speed matched to the water background. We demonstrate the proposed cancellation method with a specific case, using an array of hollow steel cylinders coated with thin silicone rubber shells. These experimental results are matched to finite element modeling predictions, confirming the scattering reduction. Additional calculations explore the optimization of the silicone coating properties. Using this approach, it is found that scattering cross-sections can be reduced by 20 dB for all wavelengths up to k0a = 0.85.

Designing acoustic transformation devices using fluid homogenization of an elastic substructure

The design of devices using finite embedded coordinate transformations presents an unique approach to control acoustic waves. Though combining the use of conformal mappings may provide a pathway to more realizable material properties, many device geometries still require combinations of density and sound speed which are unavailable in isotropic materials. Here, we present a design strategy based on a multiple scattering homogenization method to approximate the unique values required within such a device. We apply the method, using full-wave simulations, to the design of an aqueous cylindrical-to-plane wave lens, which can be constructed from simple materials.

Transparent Gradient-Index Lens for Underwater Sound Based on Phase Advance

Spatial gradients in refractive index have been used extensively in acoustic metamaterial applications to control wave propagation through phase delay. This study reports the design and experimental realization of an acoustic gradient index lens using a sonic crystal lattice that is impedance matched to water over a broad bandwidth. In contrast to previous designs, the underlying lattice features refractive indices that are lower than the water background, which facilitates propagation control based on a phase advance as opposed to a delay. The index gradient is achieved by varying the filling fraction of hollow, air-filled aluminum tubes that individually exhibit a higher sound speed than water and matched impedance. Acoustic focusing is observed over a broad bandwidth of frequencies in the homogenization limit of the lattice, with intensity magnifications in excess of 7 dB. An anisotropic lattice design facilitates a flat-faceted geometry with low backscattering at 18 dB below the incident sound pressure level. Three dimensional Rayleigh-Sommerfeld integration that accounts for the anisotropic refraction is used to accurately predict the experimentally measured focal patterns.

Low-frequency resonance of an oblate spheroidal cavity in a soft elastic medium

Axisymmetric monopole resonances of an oblate spheroidal cavity in a soft elastic medium are computed using both separation of variables and finite-element approaches. The resonances are obtained for compression wavelengths much longer than the cavity size and thus have a low-frequency character. Resonant frequencies for high-aspect-ratio oblate spheroids (either air-filled or evacuated) are found to be significantly lower than their spherical counterparts with equivalent volume. This finding contrasts with the case of an air bubble in water which features weak shape dependence. The results are relevant to the design of locally-resonant acoustic media using soft-lithography techniques with elastomers.

Underwater sound transmission through thin soft elastomers containing arrays of pancake voids: Measurements and modeling

Measurement of underwater sound transmission through thin (~750 micron) layers of the soft elastomer polydimethylsiloxane (PDMS) containing microfabricated arrays of pancake-shaped cavities is presented. Cavities are 120 microns in diameter and 5 microns in height with a nominal lattice spacing of 300 microns. A sound transmission minimum is found at 282 kHz which agrees with predictions of a finite-element model of the array and the value for monopole resonance frequency of an air-filled single pancake cavity in unbounded PDMS. This resonance is a factor of 0.62 lower than the null that would occur for spherical cavities of equivalent volume. The width of the null is also significantly broader than that which would be obtained with spherical voids. Modeling results incorporate careful measurements of attenuation for both shear and compression waves in PDMS done in a separate effort. Acoustic transmission variation as a function of lattice spacing and the number of layers is discussed. [Work sponsored by ...

Designing beampatterns with tapered leaky wave antennas

Leaky wave antennas (LWAs) have been shown to be an effective tool for frequency-steerable wave radiation in both the electromagnetic and acoustic wave regimes. LWA’s operate by modifying the impedance on a waveguide such that refraction occurs out of the waveguide at an angle corresponding to Snell’s Law. For a LWA with uniform leaking parameter across the waveguide length, that leakage angle is constant. Using analytical techniques, and by careful geometric design of the waveguide impedance, the leaked beampattern can be tailored. The process of the tapering process for an acoustic LWA is discussed here, and notional examples are presented including sidelobe reduction. [Work supported by the Office of Naval Research.]