Ultrasonic scattering by a side-drilled hole

The scattering of elastic waves by a side-drilled hole (sdh) i.e. a circular cylindrical cavity, is considered. The scattering of plane or cylindrical waves by an sdh is an old subject; here the T matrix solution is adopted. The elastic waves are excited by an ultrasonic probe and a model of such a probe is thus used. The waves from the probes are expressed as a Fourier transform, i.e. as a superposition of plane waves. These plane waves are then transformed to the cylindrical system centred at the sdh. To obtain the signal in a receiving ultrasonic probe an electromechanical reciprocity relation is used. The signal response is obtained as a double wavenumber integral and an azimuthal summation. In the far field the integrals can be calculated approximately by the stationary phase approximation. Some numerical examples are given, in particular concentrating on when this approximation is valid.