Underwater sound transmission through arrays of disk cavities in a soft elastic medium.

Scattering from a cavity in a soft elastic medium, such as silicone rubber, resembles scattering from an underwater bubble in that low-frequency monopole resonance is obtainable in both cases. Arrays of cavities can therefore be used to reduce underwater sound transmission using thin layers and low void fractions. This article examines the role of cavity shape by microfabricating arrays of disk-shaped air cavities into single and multiple layers of polydimethylsiloxane. Comparison is made with the case of equivalent volume cylinders which approximate spheres. Measurements of ultrasonic underwater sound transmission are compared with finite element modeling predictions. The disks provide a deeper transmission minimum at a lower frequency owing to the drum-type breathing resonance. The resonance of a single disk cavity in an unbounded medium is also calculated and compared with a derived estimate of the natural frequency of the drum mode. Variation of transmission is determined as a function of disk tilt angle, lattice constant, and layer thickness. A modeled transmission loss of 18 dB can be obtained at a wavelength about 20 times the three-layer thickness, and thinner results (wavelength/thickness ∼ 240) are possible for the same loss with a single layer depending on allowable hydrostatic pressure.

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.

Experimental verification of enhanced sound transmission from water to air at low frequencies.

Laboratory measurements of enhanced sound transmission from water to air at low frequencies are presented. The pressure at a monitoring hydrophone is found to decrease for shallow source depths in agreement with the classical theory of a monopole source in proximity to a pressure release interface. On the other hand, for source depths below 1/10 of an acoustic wavelength in water, the radiation pattern in the air measured by two microphones becomes progressively omnidirectional in contrast to the classical geometrical acoustics picture in which sound is contained within a cone of 13.4° half angle. The measured directivities agree with wavenumber integration results for a point source over a range of frequencies and source depths. The wider radiation pattern owes itself to the conversion of evanescent waves in the water into propagating waves in the air that fill the angular space outside the cone. A ratio of pressure measurements made using an on-axis microphone and a near-axis hydrophone are also reported and compared with theory. Collectively, these pressure measurements are consistent with the theory of anomalous transparency of the water-air interface in which a large fraction of acoustic power emitted by a shallow source is radiated into the air.

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.

Acoustical scattering by multilayer spherical elastic scatterer containing electrorheological layer.

A computational procedure for analyzing acoustical scattering by multilayer concentric spherical scatterers having an arbitrary mixture of acoustic and elastic materials is proposed. The procedure is then used to analyze the scattering by a spherical scatterer consisting of a solid shell and a solid core encasing an electrorheological (ER) fluid layer, and the tunability in the scattering characteristics afforded by the ER layer is explored numerically. Tunable scatterers with two different ER fluids are analyzed. One, corn starch in peanut oil, shows that a significant increase in scattering cross-section is possible in moderate frequencies. Another, fine poly-methyl methacrylate (PMMA) beads in dodecane, shows only slight change in scattering cross-sections overall. But, when the shell is thin, a noticeable local resonance peak can appear near ka=1, and this resonance can be turned on or off by the external electric field.

Multisector parabolic-equation approach to compute acoustic scattering by noncanonically shaped impenetrable objects.

Parabolic equation (PE) methods have long been used to efficiently and accurately model wave phenomena described by hyperbolic partial differential equations. A lesser-known but powerful application of parabolic equation methods is to the target scattering problem. In this paper, we use noncanonically shaped objects to establish the limits of applicability of the traditional approach and introduce wide-angle and multiple-scattering approaches to allow accurate treatment of concave scatterers. The PE calculations are benchmarked against finite-element results, with good agreement obtained for convex scatterers in the traditional approach, and for concave scatterers with our modified approach. We demonstrate that the PE-based method is significantly more computationally efficient than the finite-element method at higher frequencies where objects are several or more wavelengths long.

Enhanced sound transmission from water to air at low frequencies.

Excitation of acoustic radiation into the air from a low-frequency point source under water is investigated using plane wave expansion of the source spectrum and Rayleigh reflection/transmission coefficients. Expressions are derived for the acoustic power radiated into air and water as a function of source depth and given to lowest order in the air/water density ratio. Near zero source depth, the radiation into the water is quenched by the source's acoustic image, while the power radiated into air reaches about 1% of the power that would be radiated into unbounded water.

Acoustical scattering by arrays of cylinders in waveguides.

Multiple scattering of acoustic waves in a planar horizontal waveguide by finite-length cylinders is considered. Cylinder height equals the waveguide depth, and both are vertically constrained by the pressure-release boundaries. An analytically exact solution is obtained via normal mode expansion method in conjunction with the concept of the T matrix. The problem is decomposed into an infinite number of two-dimensional multiple scattering problems, modulated by waveguide mode shapes. Examples are presented for an isovelocity waveguide in which the medium is uniform and the waveguide depth is constant. It is found that, in numerical computations, including one or two evanescent modes captures the essence of the evanescent modes. Multiple scattering in the waveguide is compared with the corresponding two-dimensional case. It is concluded that, in low frequencies, the wave patterns in the two cases are very similar, with a shift in the frequency. The similarity diminishes when there are multiple propagating modes. Despite the mode mixing, some key features in the scattering as observed in the two-dimensional problem remain observable in the waveguide case.

Comparison of a subrank to a full-rank time-reversal operator in a dynamic ocean.

This paper investigates the application of time-reversal techniques to the detection and ensonification of a target of interest. The focusing method is based on a generalization of time-reversal operator techniques. A subrank time-reversal operator is derived and implemented using a discrete set of transmission beams to ensonify a region of interest. In a dynamic ocean simulation, target focusing using a subrank matrix is shown to be superior to using a full-rank matrix, specifically when the subrank matrix is captured in a period shorter than the coherence time of the modeled environment. Backscatter from the point target was propagated to a vertical 64-element source-receiver array and processed to form the sub-rank time-reversal operator matrix. The eigenvector corresponding to the strongest eigenvalue of the time-reversal operator was shown to focus energy on the target in simulation. Modeled results will be augmented by a limited at-sea experiment conducted on the New Jersey shelf in April-May 2004 measured low-frequency backscattered signal from an artificial target (echo repeater).

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.