| In this work, analytic models have been developed for two different nondestructive evaluation (NDE) applications: the characterization of spherically focused ultrasonic immersion transducers, and the prediction of the radiated wave fields of a variety of commonly used ultrasonic transducers.;When a spherically focused probe is correctly and completely characterized, its corresponding theoretical model can accurately predict the experimentally measured structure of its incident wave field. A new and efficient method for completely characterizing a spherically focused transducer and its accompanying measurement system is described. Predicted responses that make use of this method are shown to correspond very well to measured responses for a number of different commercial transducers.;The ultrasonic beam modeling work is divided into three parts. First, the problem of a planar piston ultrasonic transducer radiating at oblique incidence through a planar fluid-solid interface is studied, and two new types of beam models representing this problem are developed--a surface integral model and a boundary diffraction wave (BDW) paraxial model. The less restrictive surface integral model is used to test the validity of the BDW paraxial model, particularly in the near field and at different angles of incidence. Second, a new edge element method has been developed for numerically evaluating a variety of ultrasonic transducer beam models. This edge element model, which uses a local Fraunhofer approximation, is used to evaluate the wave fields of a focused probe in water and of a planar probe radiating at oblique incidence to a plane fluid-solid interface. Third and finally, a complete elastodynamic model of an ultrasonic angle beam shear wave transducer is presented. This model is evaluated by the edge element method, and the various transmitted mode contributions are studied and compared to more approximate models. |
