Ultrasonic pulsed beam interaction with a fluid-loaded elastic plate: Theory

Abstract

The interaction of transducer-excited ultrasonic pulsed beams with fluid-loaded elastic plates is treated with a computationally efficient analytical model. The model synthesizes the frequency-domain voltage, due to a single transducer operated in reflection (pulse-echo) mode and a pair of tranducers in transmission mode, utilizing an approach that is based on (1) expansion of transducer fields in terms of quasi-Gaussian beams modeled via the complex-source-point technique and its recent extension to finite receivers, and on (2) complex wave-number spectral decomposition and synthesis to solve the beam–structure interaction problem. First, a reference solution for the frequency-domain reflected and transmitted fields is expressed in terms of spectral integrals over two-dimensional infinite spectra of plane waves weighted by the plate reflection or transmission coefficient. Subsequent expansion in terms of a finite sum of integrals representing multiply reflected beams propagating within the plate, combined with high-frequency asymptotics and inverse Fourier transformation of the frequency-domain data, yields the time-domain voltage as a finite sum of purely compressional (P), purely shear (S), and P–S coupled arrivals. Of particular interest is the new higher-order asymptotic expansion developed to account for shear waves excited in the plate by the finite angular spectrum of beams at normal incidence. Both reference and asymptotic solutions have been implemented in numerical codes and validated against experimentally generated data. This is shown in a follow-up paper. The methodology presented here can be applied under more general conditions of transducer orientation and focusing, and also for elastic media with more than one layer.