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A simple but general solution of Navier's equation for axisymmetric shear wave propagation in a homogeneous isotropic viscoelastic medium is presented. It is well-suited for use as a forward model for some acoustic radiation force impulse based shear wave elastography applications because it does not require precise knowledge of the strength of the source, nor its spatial or temporal distribution. Instead, it depends on two assumptions: (1) the source distribution is axisymmetric and confined to a small region near the axis of symmetry, and (2) the propagation medium is isotropic and homogeneous. The model accounts for the vector polarization of shear waves and exactly represents geometric spreading of the shear wavefield, whether spherical, cylindrical, or neither. It makes no assumption about the frequency dependence of material parameters, i.e., it is material-model independent. Validation using measured shear wavefields excited by acoustic radiation force in a homogeneous gelatin sample show that the model accounts for well over 90% of the measured wavefield "energy." An optimal fit of the model to simulated shear wavefields with noise in a homogeneous viscoelastic medium enables estimation of both the shear storage modulus and shear wave attenuation to within 1%.

A new iterative time-reversal algorithm capable of identifying and focusing on multiple scatterers in a relatively small number of iterations is developed. It is recognized that the traditional iterated time-reversal method is based on utilizing power iterations to determine the dominant eigenpairs of the time-reversal operator. The convergence properties of these iterations are known to be suboptimal. Motivated by this, a new method based on Lanczos iterations is developed. In several illustrative examples it is demonstrated that for the same number of transmitted and received signals, the Lanczos iterations based approach is substantially more accurate.

A method for producing a prescribed acoustic pressure field from a piezoelectric array was investigated. The array consisted of 170 elements placed on the inner surface of a 15 cm radius spherical cap. Each element was independently driven by using individual pulsers each capable of generating 1.2 kV. Acoustic field customization was achieved by independently controlling the time when each element was excited. The set of time delays necessary to produce a particular acoustic field was determined by using an optimization scheme. The acoustic field at the focal plane was simulated by using the angular spectrum method, and the optimization searched for the time delays that minimized the least squared difference between the magnitudes of the simulated and desired pressure fields. The acoustic field was shaped in two different ways: the -6 dB focal width was increased to different desired widths and the ring-shaped pressure distributions of various prescribed diameters were produced. For both cases, the set of delays resulting from the respective optimization schemes were confirmed to yield the desired pressure distributions by using simulations and measurements. The simulations, however, predicted peak positive pressures roughly half those obtained from the measurements, which was attributed to the exclusion of nonlinearity in the simulations. [ABSTRACT FROM AUTHOR]

This paper formulates and solves a time harmonic inverse scattering problem to reconstruct the effective stiffness distribution of an adhesive bond in a layered elastic plate. The motivation is based on the assumption that localized adhesion flaws that diminish bond stiffness also tend to diminish bond strength. The formulation is based on the invariant imbedding method, applies to isotropic and anisotropic elastic layers, and is essentially that of identifying embedded acoustic sources in elastic layered structures. This paper presents two solutions for the inverse problem: the Born approximation and the exact solution. The example calculations compare the two solutions and show that when imperfections are too large in either magnitude or extent the accuracy of the Born approximation breaks down. The impact of noise and uncertainties in the background properties in the inversion is also investigated. A regularization strategy is introduced in the exact solution that controls solution sensitivity in regions with low signal to noise ratio. [ABSTRACT FROM AUTHOR]

Three-dimensional infinite elements for exterior problems of time-harmonic acoustics are developed. The infinite elements mesh only the outer boundary of the finite element domain and need not match the finite elements on the interface. A four-noded infinite element, based on separation of variables in spherical coordinates, is presented. Singular behavior of associated Legendre functions at the poles is circumvented. Numerical results validate the good performance of this approach. [ABSTRACT FROM AUTHOR]