Modeling the Ultrasonic Radiation of Shear Wave Angle Beam Transducers

The Wavefield of an Ultrasonic Angle Beam Shear Wave Transducer: An Elastodynamic Approach

“…At this point, the incident wavefields of the elastodynamic model could be evaluated through direct numerical integration procedures, but this type of evaluation would be computationally costly to do because of the two dimensional nature of the integration. By using the edge element technique discussed in earlier papers [3,7], the post stationary phaseform ofthe wavefields can be significantly simplified (numerically) by reducing the order of integration from 2-D to 1-D, thus saving computational time while retaining the same Ievel of accuracy as the more numerically intensive approaches. A paraxial assumption could also be made at this juncture [2], but in this case, a certain amount of accuracy would be lost in the very nearfield areas of the wavefield.…”

“…Over the past few years, we have turned our attention specifically to the incident wavefields produced by these transducers and investigated a number of beam models that can be applied to these types of inspection problems. Comparisons of models based on Gauss-Hermite expansions, boundary diffraction waves, paraxial and non paraxial approxirnations have been made [2,3] for unfocused transducers residing in a fluid and oriented obliquely incident to planar fluidsolid interfaces (see Figure 1a). In these models, the firstmedium was taken tobe a fluid, while in reality, angle beam transducers actually employ a contact compressional wave transducer acting on the surface of an elastic solid wedge.…”

“…By developing a more complete elastodynamic (solid-solid) transducer beam model which includes all the possible bulk wave modes in both the transducer wedge and the interrogated material, we can examine this assumption and compare the results of this latest model with previous ones that have replaced the wedge material with an equivalent fluid. The incident wavefields transmitred into a material being inspected by an angle beam shear wave transducer can be modeled in a two step process, as discussed in [2,3]. First, the wavefields in the wedge material of the transducer are determined by modeling the angle beam probe as a planar, contact transducer radiating into an isotropic, homogeneous, elastic half-space, which results in an expression for the incident displacements in the wedge that is very similar to the Rayleigh-Sommerfeld integral.…”

“…These angular spectrum integrals are evaluated by the method of stationary phase and Iead to expressions similar in form to the Rayleigh-Sommerfeld surface integral for a piston transducer in a fluid. These surface integrals can be evaluated numerically by using edge elements, as discussed in [3]. Comparisons of this latest model with the more approximate models assuming an equivalent fluid-like material for the transducer wedge will be made later in the paper.…”