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.

Analytical solution for acoustic radiation force and torque on a spheroid near a rigid or free planar boundary.

An analytical solution is developed for the acoustic radiation force and torque caused by an arbitrary sound field that is incident on a compressible spheroid of any size near a planar boundary that is either rigid or pressure release. The analysis is an extension of a recent solution for a compressible sphere near a planar boundary [Simon and Hamilton, J. Acoust.

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.

Focused Shear Wave Beam Propagation in Tissue-Mimicking Phantoms.

Objective: Ultrasound transient elastography (TE) technologies for liver stiffness measurement (LSM) utilize vibration of small, flat pistons, which generate shear waves that lack directivity. The most common cause for LSM failure in practice is insufficient shear wave signal at the needed depths. We propose to increase shear wave amplitude by focusing the waves into a directional beam.

Nonlinear propagation of quasiplanar shear wave beams in soft elastic media with transverse isotropy.

Model equations are developed for shear wave propagation in a soft elastic material that include effects of nonlinearity, diffraction, and transverse isotropy. A theory for plane wave propagation by Cormack [J. Acoust.

Longitudinal motion of focused shear wave beams in soft elastic media.

Shear waves are employed in medical ultrasound imaging because they reveal variations in viscoelastic properties of soft tissue. Frequencies below 1 kHz are required due to the substantially higher attenuation and lower propagation speeds than for compressional waves. Shear waves exhibiting particle motion in the direction of propagation, referred to as longitudinal shear waves, can be generated with longitudinal motion of a circular disk on the surface of a soft elastic medium.

Analytical solution for acoustic radiation force on a sphere near a planar boundary.

Acoustic radiation force on a sphere in an inviscid fluid near a planar boundary, which may be rigid or pressure release, is calculated using spherical wave functions to expand the total pressure field. The condition at the boundary is satisfied with the addition of a reflected wave and an image sphere. The total pressure field, which is exact in the linear approximation, is composed of the incident field, the reflected field, and the scattered fields due to the physical sphere and the image sphere.

Nonlinear piezoelectric surface acoustic waves.

The theory for nonlinear surface acoustic waves in crystals developed using Hamiltonian mechanics [Hamilton, Il'inskii, and Zabolotskaya, J. Acoust. Soc.

Born approximation of acoustic radiation force and torque on inhomogeneous objects.

The Born approximation developed previously to model acoustic radiation force and torque exerted on homogeneous compressible objects of arbitrary shape [Jerome et al., J. Acoust.

Evolution equation for nonlinear Lucassen waves, with application to a threshold phenomenon.

A nonlinear, fractional, surface wave equation with a spatial derivative of second order was developed by Kappler, Shrivastava, Schneider, and Netz [Phys. Rev. Fluids 2, 114804 (2017)] for propagation along an elastic interface coupled to a viscous incompressible liquid.

Acoustic radiation torque on a compressible spheroid.

Starting with the theoretical framework for calculating the acoustic radiation force on a compressible spheroid [Jerome et al., J. Acoust.

Acoustical characterization of a portable pneumatic infrasound source.

A portable infrasound source based on a pneumatic siren design is described. The source is capable of producing narrowband tone bursts over a frequency range of approximately 0.25-10 Hz.

Acoustic radiation force on a compressible spheroid.

The acoustic radiation force on a compressible spheroid is calculated using expansions of the scattered field in terms of both spherical and spheroidal wave functions that are matched analytically in the far field. There is no restriction on the size or impedance of the spheroid, the structure of the incident field, or the orientation of the spheroid with respect to the incident field. The form of the solution is the same as that developed previously for the radiation force on an elastic sphere, which is a summation of terms involving products of the coefficients in spherical wave expansions of the incident and scattered fields.

Acoustic radiation from an infrasonic ball-valve siren.

The concept of a ball-valve siren is developed through experimentation and theoretical modeling. The ball-valve siren is a source transducer developed for the purpose of establishing the concept of infrasound generation through the modulation of compressed air flowing through a rotating ball valve and released into the atmosphere, in the context of a siren. Directivity, frequency response, and propagation experiments were performed for the fundamental frequency component, and the results compare favorably to an empirical model based on monopole and dipole radiation.

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.

Elastic softening of sandstone due to a wideband acoustic pulse.

Elastic wave propagation experiments were performed on a thin bar sample composed of Texas "moss" sandstone in order to study nonlinear elastic effects in the time domain. The present experiments utilized a pendulous hammer to produce axially propagating transient signals with strain amplitude between 15 and 130 microstrain in the mid-audio band. Particle velocity along the bar axis was measured with a laser Doppler vibrometer, focused at various locations along the bar.

Transient solutions for the angular dependence of acoustical transmitters and receivers employing paraboloidal reflectors.

Time-domain solutions are presented for the angular dependence of waveforms in the far field of a point source at the focus of a rigid paraboloidal reflector, and also for waveforms at the focus as a function of the direction of a plane wave incident on the reflector. The main restriction is that the wavelength is small in relation to both the radius of the aperture and the minimum radius of curvature of the reflector, conditions which are satisfied for reflectors with appreciable gain. The solution in the far field due to a point source at the focus is related by the principle of reciprocity to the solution at the focus due to an incident plane wave.

Born approximation of acoustic radiation force and torque on soft objects of arbitrary shape.

When the density and compressibility of an object are similar to the corresponding properties of the surrounding fluid and the incident sound field is a standing wave, the Born approximation may be used to calculate the acoustic radiation force and torque on an object of arbitrary shape. The approximation consists of integration over the monopole and dipole contributions to the force acting at each point within the region occupied by the object. The method is applied to axisymmetric objects, for which the force and torque may be expressed as a single integral along the axis of symmetry.

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.

Acoustic radiation force on an elastic sphere in a soft elastic medium.

A theoretical framework in Lagrangian coordinates is developed for calculating the acoustic radiation force on an elastic sphere in a soft elastic medium. Advantages of using Lagrangian coordinates are that the surface of the sphere is fixed in the reference frame, and nonlinearity appears only in the stress tensor. The incident field is a time-harmonic compressional wave with arbitrary spatial structure, and there is no restriction on the size of the sphere.

Plane nonlinear shear waves in relaxing media.

Model equations with cubic nonlinearity are developed for a plane shear wave of finite amplitude in a relaxing medium. The evolution equation for progressive waves is solved analytically for a jump in stress that propagates into an undisturbed medium. Weak-shock theory is used to determine the amplitude and location of the shock when the solution predicts a multivalued waveform.

Radiation damping of, and scattering from, an arbitrarily shaped bubble.

The work by Strasberg on small volume oscillations of bubbles with arbitrary shape [J. Acoust. Soc.

Effective Gol'dberg number for diverging waves.

An effective Gol'dberg number is proposed for determining the degree of nonlinear distortion achieved in a diverging wave field. For values that are large compared with unity, the degree of nonlinear waveform distortion is virtually the same as that for a plane wave characterized by the traditional Gol'dberg number having the same numerical value. Expressions for the effective Gol'dberg number are proposed for spherical and cylindrical waves, Gaussian beams, and exponential horns.

Model for the dynamics of a spherical bubble undergoing small shape oscillations between parallel soft elastic layers.

A model is developed for a pulsating and translating gas bubble immersed in liquid in a channel formed by two soft, thin elastic parallel layers having densities equal to that of the surrounding liquid and small, but finite, shear moduli. The bubble is nominally spherical but free to undergo small shape deformations. Shear strain in the elastic layers is estimated in a way which is valid for short, transient excitations of the system.