| We study the interaction between an ultrasonic transducer and a test medium, idealized to be an elastic half-space, through a viscous couplant. The transducing element is a circular piezoelectric cylinder of class C(,6v), polarized in the thickness direction with electroded faces and insulated lateral edge. The crystal is part of an electric circuit, and the transducer is considered to be either sending or receiving, depending on whether or not a source of specified voltage is included in the circuit. The piezoelectric disc is modelled as a first order linear plate of finite extent.; In the first part of the thesis we model a transducer unit typical of those presently used in Nondestructive Testing (NDT) practice, with all of its complexities, e.g., backing and constraining casing. In the second part we model the physically simple transducer consisting of just the bare electroded piezoelectric disc. For both devices, we present the study vibration problem of the transducer/test medium configuration forced by the voltage source in the transducer circuit and an incident wave in the test medium. These problems are reduced to coupled integral equations for the torsionless axisymmetric components of the interface tractions on the crystal faces. Various approximations of the problem are also considered in an attempt to adequately model the transduction process without having to solve these integral equations.; The third part of the thesis is a summary and conclusion. |
