Elastic wave scattering in a solid half-space with a circular cylindrical hole using the Distributed Point Source Method

Ultrasonic wave scattering in a solid half-space containing a circular cylindrical hole is studied. The solid is struck by a bounded ultrasonic beam. Distributed Point Source Method (DPSM) which is a semi-analytical technique is adopted to model the ultrasonic field. A finite size transducer is used to generate the ultrasonic field. The circular hole in the solid is modeled by passive point sources. These point sources along with the point sources placed near the fluid–solid interface contribute to the scattered wave field in the solid. Even though the wave scattering by a circular hole in a solid is a classical problem this is the first time the complete variation of the scattered wave field generated by a bounded ultrasonic beam in a solid half-space with a circular hole is shown. The solution of this problem will help us to understand the distortion of the ultrasonic field in a solid and in the neighboring fluid due to the presence of a cylindrical anomaly which plays an important role in sensitivity analysis and calibration of different non-destructive testing techniques. Numerical examples for 1 MHz and 2.25 MHz transducers are given and scattered wave fields generated by holes of different diameters in an aluminum half-space are compared with the wave fields generated in the defect-free environment.