An asymptotic model for compressional and shear wave excitation in plates by ultrasonic transducers

Abstract

Pulsed beams excited and detected by ultrasonic transducers are routinely used to characterize elastic structures. An efficient model for transducer–structure interactions is presented and applied to transmission through a fluid-loaded plate with a transmitter–receiver pair. Each transducer is modeled as several complex-transducer points (CTPs) [Zeroug etal., ReviewofProgressinQNDE, edited by Thompson and Chimenti (Plenum, New York, 1994), Vol. 13], which behave as reciprocal, electroacoustic quasi-Gaussian transducers. The interaction of each CTP transmitter–receiver pair with the plate is solved by wave-number spectral decomposition and ray expansions, resulting in a sum of multiply reflected beams propagating within the plate. The resulting time-harmonic beam integrals are approximated asymptotically and transformed to the time domain to yield the received voltage as a finite sum of multiply reflected compressional (P), shear (S), and coupled (P–S) arrivals. Comparison with experiments shows that (a) three CTPs accurately model the flat circular transducers, (b) the efficient asymptotic solution is accurate when the observed arrivals are distinct in time, and (c) at normal incidence, the S and P–S arrivals which are excited by the transducers’ finite spectrum necessitate higher-order asymptotic expansions. This approach can be generalized to transducers’ arbitrary orientation, multilayered and cylindrical configurations.