Multiple reflected beam synthesis of fields excited by a high-frequency oblique beam input in an elastic plate

Transducer-excited beams provide important diagnostic tools for ultrasonic nondestructive evaluation (NDE) of elastic materials. For bonded multilayer elastic plates, an obliquely injected high-frequency compressional (P) beam creates interior dynamic fields that are sensitive to weak debonding between the layers. In an effort to clarify the wave phenomena that are operative under these conditions of excitation, a highly idealized model has been chosen wherein a lossless plate in vacuum is insonified by an internal oblique P-beam source. This problem was analyzed in a previous investigation [Lu, Felsen, and Klosner, J. Acoust. Soc. Am. 87, 42-53 (1990)] by expressing the total field in terms of a sum of P-S (vertically polarized or in-plane) coupled normal modes. While the resulting field assumed oscillatory modal patterns at interior cross sections far from the source region, the modally synthesized field near the source clearly outlined profiles interpretable as incident and singly or multiply reflected P-S coupled beams. The problem is therefore studied here directly by Gaussian beam tracing as implemented via our previously employed complex ray field algorithm. The results clarify the observed phenomena by revealing the successive buildup from initially well-resolved beams into oscillatory mode patterns synthesized by overlapping multiples. For the same idealized model, the beam algorithm has been applied elsewhere to the detection and identification of weak debonding in a layered plate [Felsen and Zeroug, J. Acoust. Soc. Am. 90, 1527-1538 (1991)]. With an understanding of the physical mechanisms that arise in the beam-to-mode conversion, one may now explore how their utility is affected under realistic NDE conditions.