Analytical modeling for fast simulations of ultrasonic measurements on fluid-loaded layered elastic structures

Quantitative modeling of ultrasonic pulse-echo and pitch-catch measurements for non-destructive evaluation (NDE) of bulk or layered fluid-immersed elastic materials is important for optimal measurement design, data interpretation, and parameter inversion. Just as important is the computational efficiency of the resulting numerical algorithms to ensure that they are exploited effectively. For defect-free configurations consisting of planar and cylindrical homogeneous and isotropic layers, analytical modeling, employing spectral integral decomposition and synthesis, offers a powerful tool to meet this requirement. The analytical approach allows the expression of the receiving transducer voltage and the beam-structure interaction in terms of a spectral wavenumber integral. Within this representation, transducer beams are specified in terms of their pressure or normal velocity spectra or, alternatively and more conveniently, in terms of Gaussian beams generated through the complex transducer point (CTP) technique. The voltage integrals may be implemented numerically or reduced to closed-form solutions via high frequency asymptotic techniques. This article summarizes the theory, discusses its numerical implementation, and illustrates its applications through two time-domain measurements. The first pertains to a pulse-echo measurement conducted from inside a cylindrically layered structure and for which the theoretical predictions are successfully validated by experimental data. The second pertains to a pitch-catch measurement to generate and detect leaky Lamb waves in a plate. For this latter case, uniform asymptotics, validated by comparisons with numerical integration, is used to isolate the contributions of the various Lamb modes to the total voltage.