Analytical solutions for acoustic vortex beam radiation from planar and spherically focused circular pistons.

Analytical solutions for acoustic vortex beams radiated by sources with uniform circular amplitude distributions are derived in the paraxial approximation. Evaluation of the Fresnel diffraction integral in the far field of an unfocused source and in the focal plane of a focused source leads to solutions in terms of an infinite series of Bessel functions for orbital numbers ℓ>-2. These solutions are reduced to closed forms for 0≤ℓ≤4, which correspond to orbital numbers commonly used in experiments.

Paraxial and ray approximations of acoustic vortex beams.

A compact analytical solution obtained in the paraxial approximation is used to investigate focused and unfocused vortex beams radiated by a source with a Gaussian amplitude distribution. Comparisons with solutions of the Helmholtz equation are conducted to determine bounds on the parameter space in which the paraxial approximation is accurate. A linear relation is obtained for the dependence of the vortex ring radius on the topological charge, characterized by its orbital number, in the far field of an unfocused beam and in the focal plane of a focused beam.

Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform.

This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression.

Controlling Displacement Fields in Polar Willis Solids via Gauge Transformations.

Rigid-body displacement and deformation constitute the total displacement field of a solid. Harnessing the former calls for well-organized kinematic elements, and controlling the latter allows for creation of shape-morphing materials. A solid capable of simultaneously controlling both rigid-body displacement and deformation remains unknown.

Exact radiation boundary conditions to determine the complex wavenumber of an underwater acoustic leaky wave antenna.

Underwater elastic leaky wave antennas (LWAs) steer acoustic energy as a function of frequency by exploiting fluid-solid coupling. LWAs present a modeling challenge due to complex radiation impedance on the waveguide surface that leads to changes in dynamic response. This work presents an approach to model underwater LWAs that considers an elastic unit cell surrounded by a fluid domain and includes a radiation boundary condition to simulate an open boundary.

Emerging topics in nanophononics and elastic, acoustic, and mechanical metamaterials: an overview.

This broad review summarizes recent advances and "hot" research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25-27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a "snapshot" of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article.

Introduction to the special issue on Additive Manufacturing and Acoustics.

Additive manufacturing (AM) has expanded to a wide range of applications over the last few years, and acoustic applications are no exception. This article is an introduction to the special issue of the Journal of the Acoustical Society of America on AM and acoustics. To provide background to the reader, a brief introduction to the manufacturing approach of AM is included.

Robust design of an asymmetrically absorbing Willis acoustic metasurface subject to manufacturing-induced dimensional variations.

Advancements in additive manufacturing (AM) technology are promising for the creation of acoustic materials. Acoustic metamaterials and metasurfaces are of particular interest for the application of AM technologies as theoretical predictions suggest the need for precise arrangements of dissimilar materials within specified regions of space to reflect, transmit, guide, or absorb acoustic waves in ways that exceed the capabilities of currently available acoustic materials. This work presents the design of an acoustic metasurface (AMS) with Willis constitutive behavior, which is created from an array of multi-material inclusions embedded in an elastomeric matrix, which displays the asymmetric acoustic absorption.

Physical Observation of a Robust Acoustic Pumping in Waveguides with Dynamic Boundary.

Research on breaking time-reversal symmetry to realize one-way wave propagation is a growing area in photonic and phononic crystals and metamaterials. In this Letter, we present physical realization of an acoustic waveguide with spatiotemporally modulated boundary conditions to realize nonreciprocal transport and acoustic topological pumping. The modulated waveguide inspired by a water wheel consists of a helical tube rotating around a slotted tube at a controllable speed.

Numerical study of acoustic focusing using a bianisotropic acoustic lens.

Materials with sub-wavelength asymmetry and long-range order have recently been shown to demonstrate acoustical properties analogous to electromagnetic bianisotropy. One characteristic of bianisotropic acoustic media is the existence of direction-dependent acoustic impedance. Therefore, the magnitude and phase of the acoustic fields transmitted through bianisotropic acoustic media are dependent on the direction of bianisotropic polarization.

An active mechanical Willis meta-layer with asymmetric polarizabilities.

Willis materials exhibit macroscopic cross-coupling between particle velocity and stress as well as momentum and strain. However, Willis coupling coefficients designed so far are intrinsically coupled, which inhibits their full implementation in structural dynamic applications. This work presents a means to eliminate these limitations by introducing an active scatterer in a mechanical meta-layer that exploits piezoelectric sensor-actuator pairs controlled by digital circuits.

Acoustic response for nonlinear, coupled multiscale model containing subwavelength designed microstructure instabilities.

Nonperiodic arrangements of inclusions with incremental linear negative stiffness embedded within a host material offer the ability to achieve unique and useful material properties on the macroscale. In an effort to study such types of inclusions, the present paper develops a time-domain model to capture the nonlinear dynamic response of a heterogeneous medium containing a dilute concentration of subwavelength nonlinear inclusions embedded in a lossy, nearly incompressible medium. Each length scale is modeled via a modified Rayleigh-Plesset equation, which differs from the standard form used in bubble dynamics by accounting for inertial and viscoelastic effects of the oscillating spherical element and includes constitutive equations formulated with incremental deformations.

Non-reciprocal wave propagation in mechanically-modulated continuous elastic metamaterials.

Acoustic and elastic metamaterials with time- and space-dependent effective material properties have recently received significant attention as a means to induce non-reciprocal wave propagation. Recent analytical models of spring-mass chains have shown that external application of a nonlinear mechanical deformation, when applied on time scales that are slow compared to the characteristic times of propagating linear elastic waves, may induce non-reciprocity via changes in the apparent elastic modulus for perturbations around that deformation. Unfortunately, it is rarely possible to derive analogous analytical models for continuous elastic metamaterials due to complex unit cell geometry.

Acoustic scattering from a fluid cylinder with Willis constitutive properties.

A material that exhibits Willis coupling has constitutive equations that couple the pressure-strain and momentum-velocity relationships. This coupling arises from subwavelength asymmetry and non-locality in heterogeneous media. This paper considers the problem of the scattering of a plane wave by a cylinder exhibiting Willis coupling using both analytical and numerical approaches.

Frequency-dependent behavior of media containing pre-strained nonlinear inclusions: Application to nonlinear acoustic metamaterials.

One emerging research area within the fields of acoustic and elastic metamaterials involves designing subwavelength structures that display elastic instabilities in order to generate an effective medium response that is strongly nonlinear. To capture the overall frequency-dependent and dispersive macroscopic response of such heterogeneous media with subwavelength heterogeneities, a theoretical framework is developed that accounts for higher-order stiffnesses of a resonant, nonlinear inclusion that varies with a macroscopic pre-strain, and the inherent inertia associated with an inclusion embedded in a nearly incompressible elastic matrix material. Such a model can be used to study varying macroscopic material properties as a function of both frequency and pre-strain and the activation of such microscale instabilities due to an external, macroscopic loading, as demonstrated with a buckling metamaterial inclusion that is of interest due to its tunable and tailorable nature.

Broadband focusing of underwater sound using a transparent pentamode lens.

An inhomogeneous acoustic metamaterial lens based on spatial variation of refractive index for broadband focusing of underwater sound is reported. The index gradient follows a modified hyperbolic secant profile designed to reduce aberration and suppress side lobes. The gradient index (GRIN) lens is comprised of transversely isotropic hexagonal microstructures with tunable quasi-static bulk modulus and mass density.

Experimental evidence of Willis coupling in a one-dimensional effective material element.

The primary objective of acoustic metamaterial research is to design subwavelength systems that behave as effective materials with novel acoustical properties. One such property couples the stress-strain and the momentum-velocity relations. This response is analogous to bianisotropy in electromagnetism, is absent from common materials, and is often referred to as Willis coupling after J.

Reciprocity, passivity and causality in Willis materials.

Materials that require coupling between the stress-strain and momentum-velocity constitutive relations were first proposed by Willis (Willis 1981 , 1-11. (doi:10.1016/0165-2125(81)90008-1)) and are now known as elastic materials of the Willis type, or simply Willis materials.

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure.

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field.

A high transmission broadband gradient index lens using elastic shell acoustic metamaterial elements.

The use of cylindrical elastic shells as elements in acoustic metamaterial devices is demonstrated through simulations and underwater measurements of a cylindrical-to-plane wave lens. Transformation acoustics of a circular region to a square dictate that the effective density in the lens remain constant and equal to that of water. Piecewise approximation to the desired effective compressibility is achieved using a square array with elements based on the elastic shell metamaterial concept developed by Titovich and Norris [J.

Subwavelength acoustic metamaterial panels for underwater noise isolation.

Acoustically thin metamaterial underwater noise isolation panels have been developed that provide as much as 16 dB of noise isolation for a panel with a thickness just 160th of the wavelength in the host medium (fresh water) at 2.5 kHz. The panels are composed of thin layers of neoprene rubber and polyoxymethylene containing air-filled voids.