Numerical Modeling and Imaging of Three-Dimensional Transducer Fields in Anisotropic Materials

Piezoelectric transducers are the basic tool for ultrasonic NDE applications and are commercially available in a wide variety of sizes, shapes and frequencies. However, the information that is typically provided for these transducers by the vendors is of limited value. This is especially true when it comes to testing of anisotropic structural materials. In this paper, a previously developed methodology to map radiation fields for piezoelecetric transducers is applied to the imaging of three-dimensional transducer fields generated in anisotropic propagation media. The processed data files are calculated for transversely (multicrystalline) isotropic materials via the Generalized Point-Source-Synthesis (GPSS) method. The synthetic data is transferred to an imaging workstation, where the 3D-transducer fields are displayed using commercially available graphic packages. The fields of circular contact-transducers of several frequencies are shown for different austenitic weld material configur ations

Real Time Parallel Computation and Visualization of Ultrasonic Pulses in Solids

Parallel processing has changed the way much computational physics is done. Areas such as condensed matter physics, fluid dynamics, and other fields are making use of massively parallel computers to solve immense and important problems in new ways. Simulating wave propagation is another area that has benefited through the use of parallel processing. This is graphically illustrated in this article by various numerical simulations of ultrasonic pulses propagating through solids carried out on a massively parallel computer. These computations are accompanied by visualizations of the resulting wavefield. The calculations and visualizations, together, can be completed in only seconds to several minutes and compare well with experimental data. The computations and parallel processing techniques described should be important in related fields, such as geophysics, acoustics, and mechanics

Obituaries

In elastic materials the propagation of ultrasonic waves is governed by the Christoffers equation, which relates the displacement vector as a function of time and position to the stiffness tensor at that point. If the material is inhomogeneous, an analytical solution of the partial differential equation becomes exceedingly difficult or impossible, especially in the presence of non-trivial boundary or initial conditions. Finite Difference Equations (FDE) provide a very convenient tool for the solution of partial differential equations (PDE’s) in media, in which the physical properties are homogeneous or vary continuously, such as Epstein Layers. Otherwise the use of FDE’s may be justified only as an approximation. In fact, for the conversion of derivatives into finite differences, a “smoothing” of the variables across the interfaces is required and, if the discontinuity is sharp, severe errors or ambiguities may result [1,2]