A paraxial theory for the propagation of ultrasonic beams in anisotropic solids

Abstract

The necessity of nondestructively inspecting cast steels, weldments, composites, and other inherently anisotropic materials has stimulated considerable interest in wave propagation in anisotropic media. Here, the problem of an ultrasonic beam traveling in an anisotropic medium is formulated in terms of an angular spectrum of plane waves. Through the use of small angle approximations, the integral representation is reduced to a summation of Gauss-Hermite eigensolutions. The anisotropic effects of beam skew and excess beam divergence enter into the solution through parameters that are simply interpreted in terms of the slowness surface. Both time harmonic and pulsed solutions are discussed. Formulas are also presented for transmission of a beam through a curved interface between two media. Examples are given illustrating how this method may be applied to predicting beam patterns during ultrasonic inspections.

Acoustic solitons: A robust tool to investigate the generation and detection of ultrafast acoustic waves

“…μ(T ) is the viscosity which may include an effective Herring process coefficient [21] but does not encompass others attenuation processes for UAP in crystals [17,22]. ξ 2 is a (dimensionless) diffraction strength coefficient such that ξ 2 = 1 when the elastic tensor is not isotropic [4,23]. Equation (1) describes the effect of viscosity and dispersion on the nonlinear propagation of an acoustic pulse with a finite transverse profile within the paraxial approximation.…”

Ultrasonic Wave Propagation through Nozzles and Pipes with Claddings around their Inner Walls

“…Figure 1 shows the cross-sectional area of a pipe or nozzle, and the clad geometry assumed in this study. As equations (1)(2) show, the clad surfaces and the pipe or nozzle geometry can easily be define with seven measurable parameters. This simple analytical description of the geometry of the cross-sectional area saves computation time when using the model.…”

Predictions of Pulse-Echo Ultrasonic Signals from Cracks Observed Through an Interface with a Step Discontinuity: Comparison with Experiments

“…The first stage consist of computation of pressure field at grid points over the rough interface. In this stage, a circular piston transducer is assumed and the field is computed using Gauss-Hermite beam Model [3]. Also, in this stage, the Poynting vector at each grid point is found.…”