With the gain in momentum of the structural health monitoring field in the last two decades, the popularity of ultrasonic nondestructive testing (NDT) has grown. However, ultrasonic NDT requires an expert to perform the testing and can be time consuming and costly when measured wave patterns in testing become extremely complex. A computer simulation of these tests can be utilized as a guide during actual evaluations or as a tool to train technicians. Presented in this dissertation is the development of models which simulate such acoustic phenomena as may arise in NDT. These models were developed using the distributed point source method (DPSM) for its proven capability to represent ultrasonic fields.Four sets of boundary conditions that arise from different types of commonly used acoustic transducers are modeled, enabling the visualization of the ultrasonic fields produced by the transducers. The transducer models exhibit good agreement with existing analytical solutions.In addition, the effect of a small cavity located at or near the focal point of an acoustic microscope is discussed. For this application the DPSM technique is modified so that inversion of a large global matrix is avoided, significantly improving the computational efficiency. The model shows that, as the pressure goes to zero, the velocity increases at the location of a cavity. Simulations demonstrate that the microscope is able to sense changes in position of the cavity by variations in the measured ratio of reflected to incident acoustic force.The field generated by an interferometric acoustic microscope is also presented. Qualitative agreement between the DPSM model and the experimental results of fields generated in a homogeneous fluid are obtained for a three-element lens. In the presence of a solid interface, the pressure on the edges of a converging beam near the fluid-solid interface is greater for a three-element lens than for single-element lens. A multi-element lens is also shown to exhibit oscillations in the pressure slightly above the interface.

The distributed point source method, or DPSM, developed in the last decade has been used for solving various engineering problems-such as elastic and electromagnetic wave propagation, electrostatic, and fluid flow problems. Based on a semi-analytical formulation, the DPSM solution is generally built by superimposing the point source solutions or Green's functions. However, the DPSM solution can be also obtained by superimposing elemental solutions of volume sources having some source density called the equivalent source density (ESD). In earlier works mostly point sources were used. In this paper the DPSM formulation is modified to introduce a new kind of ESD, replacing the classical single point source by a family of point sources that are referred to as quantum sources. The proposed formulation with these quantum sources do not change the dimension of the global matrix to be inverted to solve the problem when compared with the classical point source-based DPSM formulation. To assess the performance of this new formulation, the ultrasonic field generated by a circular planer transducer was compared with the classical DPSM formulation and analytical solution. The results show a significant improvement in the near field computation.

Elastic Wave propagation in structures with irregular boundaries is studied by transforming the plates with irregular surfaces to sinusoidal wave-guides. Guided elastic wave in a two-dimensional periodically corrugated plate is studied analytically. The plate material is considered as homogeneous, isotropic and linearly elastic. In a periodically corrugated wave-guide, all possible spectral orders of wave numbers are considered. The dispersion equation is obtained by applying the traction free boundary conditions at the two surfaces. The analysis is carried out in the wave-number domain for both symmetric and anti-symmetric modes. Non-propagating 'stop bands' and propagating 'pass bands' are investigated. Experimental analyses with two different pairs of transducers are also performed and compared with the results from the mathematical analysis. Newly developed semi-analytical DPSM technique has been also adopted in this dissertation to model the ultrasonic field in sinusoidally corrugated plate. Distributed Point Source Method (DPSM) is gradually gaining popularity in the field of Non-Destructive Evaluation (NDE). DPSM can be used to calculate the ultrasonic field (pressure, velocity and displacement in a fluid or stress and displacement in a solid) generated by ultrasonic transducers. So far the technique has been used to model ultrasonic field in homogeneous or multilayered fluid structures. In this dissertation the method is extended to model the ultrasonic field generated in both fluid and solid media. The Prime objective of using DPSM technique in this dissertation is to model the ultrasonic field generated in the corrugated wave guide. This method has never been used to model ultrasonic field in solids. Development of stress and displacement Green's functions in solids are presented. In addition to the wave propagation problem in the sinusoidal wave guide, a few unsolved problems such as ultrasonic field generated by bounded acoustic beams in multilayered fluid structures, near a fluid-solid interface and in flat solid isotropic plates are also presented in this dissertation.

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