Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Aerospace Engineering

First Advisor

R. Bruce Thompson


The recent advances in the field of ultrasonic nondestructive inspection have demanded a more precise knowledge of the propagation of sound beams within materials. Quantitative models for propagation of ultrasonic fields from a transducer can be used as tools to both analyze the inspection data and to predict inspection results. An approximate Gauss-Hermite model was developed a few years ago to predict the ultrasonic fields radiated into isotropic and anisotropic materials, through planar or simply curved interfaces by focused or unfocused transducers. The paraxial approximation used in the development of that model has allowed many functions to be evaluated analytically, thus, the model has the advantage of being computationally efficient. The Gauss-Hermite model has already been tested and verified for beam propagation through a single medium. However, there have been concerns about the performance of the model in multilayered media, and about the overall accuracy of the Gauss-Hermite solution. In the papers contained in this dissertation, more intense studies are presented evaluating the validity of the Gauss-Hermite model in a multilayered medium. First, a method of finding the elastic constants of anisotropic materials is presented. These elastic constants are important inputs to the Gauss-Hermite model. To validate the Gauss-Hermite beam model in multilayered media, comparisons have been made between its predictions and those found by the finite element method, which provides a more exact solution. The structures considered combine both isotropic and anisotropic layers. The comparison of the model with the finite element method showed good agreement around the central ray direction. Due to the use of the Fresnel approximation in the solution, the accuracy of the Gauss-Hermite model degrades as one moves away from the forward propagation direction. However, since most of the energy is concentrated in the vicinity of the central ray, which is the portion of the beam used in most NDE inspections, this problem does not appear to be too severe. To demonstrate the application of the Gauss-Hermite model to a real problem, it was used for sizing delaminations in a multilayered composite structure. This method, which utilizes the reflected signal from the delamination, showed considerable improvement over the traditional sizing method. Finally, the model in conjunction with a local ray tracing procedure, was also used to predict the ultrasonic field beyond an irregularly shaped interface (step discontinuity). The outcome of this study demonstrated a good agreement between the model predictions and experiment. Overall, this model has a good potential for being used in a variety of ultrasonic inspections.



Digital Repository @ Iowa State University,

Copyright Owner

Ali Minachi



Proquest ID


File Format


File Size

173 pages