The transient wave field of an angled shear wave probe exciting the surface of the object is shown to be a segment of line load, with appropriate signature and amplitude distribution, travelling supersonically to shear wave speed.

Much literature on moving point and line loads is available [1], [2], [3]. Pulsed transducers on a half space also receive lot of attention although most models assume fluid acoustics [4]. Especially for a solid halfspace focus is on obtaining a computationally attractive model [5]. In general, far less attention seems to be given to segments of moving line load or angled probes.

In this work we elaborate on a moving segment of line load by applying it as a model for an angled shear wave probe. These are especially used in long range NDE and create an angled shear wave beam in the loaded object.

The model is adaptable to different types of probes and is subsequently rendered computationally attractive and comprehensible after imposing far field conditions. Influence of load speed, frequency and amplitude distribution can be deduced from the resulting far field expression. The model has been elaborated for a linear elastic plate using a generalized ray tracing technique with application of the Cagniard-de Hoop method. The exact solution may be interpreted as a superposition of time-sequentially activated surface point forces. This solution allows the application of fitted data, obtained from opto-acoustic laser measurements, for source wavelet and amplitude distribution.

Because our prime interest is in the far field the different wave quantities are sufficiently decoupled and also allow wave front expansions for the short pulses. The model is verified with practical measurements of the directivity of two types of angled probes. A good agreement with measurements is obtained.

A solution to the problem of large computational effort for exact theory is found in a paraxial approximation for the geometrical attenuation of rays in the loaded plate.

This allows integration over the source area to be conducted over line segments of which the angles vary with observation angle.

The resulting expression is a temporal convolution of a paraxial ray with a mapping function which incorporates the geometrical properties of the source. For a uniform amplitude distribution and convenient source shape this mapping function can be found analytically.

It turns out that the far field directivity of a probe may be characterized by a single parameter (referred to as focus gate) which is found by simple geometrical considerations.

When varied within reasonable limits the source wavelet and amplitude distribution are then shown to only determine details in the directivity pattern.

The validity of the far field model at moderate distances is established with a near field limit which is expressed in terms of the product of dominating frequency and focus gate.

REFERENCES

1. D. C. Gakenheimer and J. Miklowitz (1969), "Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface", Journ. of Appl. Mech. pp. 505-515, September 1969
2. R. G. Payton, "Transient motion of an elastic half-space due to a moving surface line-load", Int. J. Engng. Sc.., Vol. 5, pp. 49-79, 1967
3. L. M. Brock, "Wave propagation in an elastic half-space due to surface pressure over a non-uniformly changing circular zone", Quarterly of Applied Mathematics, pp. 37-49, April 1980
4. G. R. Haris, "Transient field of a baffled planar piston having an arbitrary vibration amplitude distribution", J. Acoust. Soc. Am., Vol. 70, July 1981
5. A. Lhemery, "A model for the transient ultrasonic field radiated by an arbitrary loading in a solid", J. Acoust. Soc. Am., Vol. 96, December 1994