Reciprocity Theories for Flaw Analysis

A new method of theoretical analysis based on the use of the reciprocity theorem has been developed. With this technique, one can predict the signal scattered by a flaw from one transducer to another in terms of the signals at the actual electrical terminals. The technique is particularly useful for dealing with focused beams and for taking account of near field and far field excitation and reception. We have applied this technique, using static assumptions, to determine scattering of a Rayleigh wave from a penny-shaped crack; by using the Born approximation we have determined the scattering of Rayleigh waves from a cylindrical hole. We have also used the theory to indicate the type of reflected signals we would expect from a focused beam illuminating a crack, and the peaks in the reflection characteristics as a function of frequency due to resonant modes of the flaws. The technique can be adapted for variational calculations. Basic variational theories have been derived but have not been applied to practical problems yet