This work presents numerical models for wave propagation applied to the nondestructive testing of materials. The numerical models developed are based on a physical discretization approach called the Transmission Line Matrix method (TLM). The method replaces a continuous system by a network or an array of lumped elements. The derivation of the scattering matrix, the key element for a TLM algorithm, was performed in this dissertation in three approaches: (a) starting from first principles: as a Finite Difference Time Domain scheme; (b) using the method of moment theory; (c) and based on the equivalent representation of the wave equation as an electric circuit. Numerical modeling was carried out for frequencies that are commonly used in ultrasound and microwave nondestructive testing (3.5MHz–20GHz). The acoustic and electrical impedance profiles of multi-layer structures analyzed are similar to those found in nondestructive evaluation and in medical imaging. This work includes the ultrasonic investigation of a multi-layer bearing and the in-vitro ultrasonic imaging of biological tissues. Structures with artificial flaws are also modeled. The TLM numerical models for array probes for microwave and ultrasonic inspection are developed. Different shapes for the incident pulse are considered in the numerically generated images. A comparison between real and numerically generated images is provided for each structure considered.; The experimental data obtained by the author are used to validate the numerical models presented in this work. The models developed and described in this dissertation have proven their viability giving accurate results when compared to analytical solutions where these solutions are available and when compared to experimental results obtained for geometries that do not allow an analytical solution.
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