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.

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.

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.

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.

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.

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.

Models of cylindrical bubble pulsation.

Three models are considered for describing the dynamics of a pulsating cylindrical bubble. A linear solution is derived for a cylindrical bubble in an infinite compressible liquid. The solution accounts for losses due to viscosity, heat conduction, and acoustic radiation.

Model for bubble pulsation in liquid between parallel viscoelastic layers.

A model is presented for a pulsating spherical bubble positioned at a fixed location in a viscous, compressible liquid between parallel viscoelastic layers of finite thickness. The Green's function for particle displacement is found and utilized to derive an expression for the radiation load imposed on the bubble by the layers. Although the radiation load is derived for linear harmonic motion it may be incorporated into an equation for the nonlinear radial dynamics of the bubble.

Green's functions for a volume source in an elastic half-space.

Green's functions are derived for elastic waves generated by a volume source in a homogeneous isotropic half-space. The context is sources at shallow burial depths, for which surface (Rayleigh) and bulk waves, both longitudinal and transverse, can be generated with comparable magnitudes. Two approaches are followed.

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations.

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles.

Weakly nonlinear oscillations of a compliant object buried in soil.

A nonlinear model equation in Rayleigh-Plesset form is developed for volume oscillations of a compliant object buried close to the surface in soil. The equation takes into account the stress-free boundary condition on the surface of the ground. The model is fully nonlinear given exact relations for the elastic potential energy stored in deformation of the object and the soil.

Model of coupled pulsation and translation of a gas bubble and rigid particle.

A model of the interaction of a spherical gas bubble and a rigid spherical particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model accounts for pulsation and translation of the bubble as well as translation of the particle in an infinite, incompressible liquid. The model derived here is accurate to order R(5)d(5), where R is a characteristic radius and d is the separation distance between the bubble and particle.

Nonlinear frequency shifts in acoustical resonators with varying cross sections.

The frequency response and nonlinear resonance frequency shift of an acoustical resonator with losses and having a varying cross section were investigated previously using Lagrangian mechanics and perturbation for resonator shapes that are close to cylindrical [M. F. Hamilton, et al.

Bubble growth by rectified diffusion at high gas supersaturation levels.

For high gas supersaturation levels in liquids, on the order of 300% as predicted in capillaries of marine mammals following a series of dives [D. S. Houser, R.

Cubic nonlinearity in shear wave beams with different polarizations.

A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal.

Motion of a solid sphere in a viscoelastic medium in response to applied acoustic radiation force: Theoretical analysis and experimental verification.

The motion of a rigid sphere in a viscoelastic medium in response to an acoustic radiation force of short duration was investigated. Theoretical and numerical studies were carried out first. To verify the developed model, experiments were performed using rigid spheres of various diameters and densities embedded into tissue-like, gel-based phantoms of varying mechanical properties.

Nonlinear surface waves in soft, weakly compressible elastic media.

Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust.

Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics.

Two models of interacting bubble dynamics are presented, a coupled system of second-order differential equations based on Lagrangian mechanics, and a first-order system based on Hamiltonian mechanics. Both account for pulsation and translation of an arbitrary number of spherical bubbles. For large numbers of interacting bubbles, numerical solution of the Hamiltonian equations provides greater stability.

Modifications of the equation for gas bubble dynamics in a soft elastic medium.

A model equation for the oscillation of a pressurized gas bubble in a nonlinear incompressible elastic medium [Emelianov et al., J. Acoust.

Gas bubble and solid sphere motion in elastic media in response to acoustic radiation force.

The general approach to estimate the displacement of rounded objects (specifically, gas bubbles and solid spheres) in elastic incompressible media in response to applied acoustic radiation force is presented. In this study, both static displacement and transient motion are analyzed using the linear approximation. To evaluate the static displacement of the spherical inclusion, equations coupling the applied force, displacement, and shear modulus of the elastic medium are derived.

Nonlinear dynamics of a gas bubble in an incompressible elastic medium.

A nonlinear model in the form of the Rayleigh-Plesset equation is developed for a gas bubble in an essentially incompressible elastic medium such as a tissue or rubberlike medium. Two constitutive laws for the elastic medium are considered: the Mooney potential, and Landau's expansion of the strain energy density. These two constitutive laws are compared at quadratic order to obtain a relation between their respective elastic constants.

Thermal effects on acoustic streaming in standing waves.

Acoustic streaming generated by standing waves in channels of arbitrary width is investigated analytically. In a previous paper by the authors [J. Acoust.

Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary width.

An analytic solution is derived for acoustic streaming generated by a standing wave in a viscous fluid that occupies a two-dimensional channel of arbitrary width. The main restriction is that the boundary layer thickness is a small fraction of the acoustic wavelength. Both the outer, Rayleigh streaming vortices and the inner, boundary layer vortices are accurately described.

Nonlinear two-dimensional model for thermoacoustic engines.

A two-dimensional model and efficient solution algorithm are developed for studying nonlinear effects in thermoacoustic engines. There is no restriction on the length or location of the stack, and the cross-sectional area of the resonator may vary with position along its axis. Reduced model equations are obtained by ordering spatial derivatives in terms of rapid variations across the pores in the stack, versus slow variations along the resonator axis.