Geometrical Acoustics in a Heterogeneous Anisotropic Elastic Solid: Application to a Wavy Composite

Karal and Keller [1] developed the geometrical acoustics for wave propagation in a heterogeneous isotropic medium, generally adopting the methods used in geometrical optics [2,3]. It is very difficult to find a solution for wave propagation in a heterogeneous anisotropic medium. Here, instead of finding an exact solution, we extend the geometrical acoustics to a heterogeneous anisotropic medium to untangle the behavior of wave fronts spreading into an undisturbed region. The eikonal equation which contains information of the phase and group velocities, along with the transport equation which governs the amplitude of propagating waves, are derived. For a one-dimensionally heterogeneous anisotropic solid, wave propagation is two dimensional and it is possible to obtain closed-form analytic formulas for the ray path and travel time of a ray. These formulas are applied to find the path and travel time of rays generated from a pointlike source and detected by a small detector. The predicted arrival times agree well with observed values

Crack Length Determination by Ultrasonic Methods

Accurate calculation of the stress intensity factor on a given component under load relies on an accurate size determination of the flaws present in the component. The challenge to the NDE community has been development of reliable techniques to provide that accurate size determination. Many research groups have investigated this problem using ultrasonic methods with summaries of their techniques and results provided by various authors [1–3]. In general, the techniques developed fall into three general categories; (1) determination of crack length from signal amplitude measurements, (2) determination of crack length from time-of-flight measurements, and (3) determination of crack length using diffracted waves. Sketches of representative techniques in each category are shown in Figure 1

Theoretical Study of High Frequency Ultrasonic Wave Attenuation in Polycrystalline Materials

Three different regimes for scattering of ultrasonic waves in poly-crystalline materials exist, depending on the ratio of the mean grain size to the wavelength: (i) the low frequency (Rayleigh) region with scattering-induced attenuation proportional to the fourth power of the frequency and to the cube of the mean grain diameter, (ii) the medium frequency (stochastic) region with scattering proportional to the square of the frequency and to the mean grain diameter, and (iii) the high-frequency (geometric) region with scattering independent of frequency