Transient Radiation Pattern of Ultrasonic Transducers on Elastic Half-Spaces

Summary

The Cagniard-de Hoop method is applied to Lamb’s problem of the impulsive line and point source on an elastic half space leading to analytical expressions for the longitudinal and transverse wave components throughout the half-space without any approximation. For realistic transducer excitation broadband radiation patterns are obtained by convolution and compared to the time harmonic far-field patterns of Miller-Pursey and Roderick; they include the headwave influence and indicate a near- to far-field behavior even for idealized point- and line sources.

The theory is then extended to real transducer geometries, i.e. finite aperture sizes. Included is also a phase variation within the aperture thus simulating angle probes. The occurence of a first order pole in the mathematical expressions is physically interpreted as the direct contribution from the aperture to be distinguished from the edge contributions. The existence of a longitudinal surface wave is due to this pole.