Two- and three-dimensional complex transducer-point analysis of beam reflection from anisotropic plates

In this paper a frequency-domain analysis of the fluid-immersed plate reflection spectrum in which the transmitter and receiver acoustic beams are modeled with complex transducer points is presented. Lamb wave dispersion in the plate forms the major structural features of the reflection spectra. By assuming a linear dependence of the Fresnel length on the frequency for a flat piston transducer, the complex transducer point technique can be employed over a wide frequency range. With the aid of the reciprocity theorem for electroacoustic transducers, a rigorous three-dimensional (3D) expression for the receiver voltage in a pitch-catch transducer arrangement has been derived by using a pair of transmitting and receiving complex transducer points. The calculations are supported by the results of numerous experiments on both isotropic and anisotropic materials in various measurement geometries. The conditions under which a 3D calculation is important are demonstrated, and comparison with a simpler 2D calculation is made. The model calculation is also applied to illuminate several issues related to materials characterization. (C) 2000 Acoustical Society of America. [S0001-4966(00)02612-6].