Irradiation of an elastic plate by a finite-amplitude sound beam with applications to nondestructive evaluation

This dissertation describes an investigation of nonlinear effects associated with the interaction of ultrasound with plates. The overriding goal is to assess the potential for using immersion techniques to measure the nonlinear acoustical parameters of plates. Three measurement configurations are described, with both theory and experiment reported. Effects of weak nonlinearity are included in the theoretical models. In the first configuration, the goal is to characterize the nonlinear elastic response of an isotropic, homogeneous plate. Plate resonances were used to enhance the nonlinear acoustical response. An experiment was performed with an aluminum plate in water, but nonlinearity due to wave propagation in the plate could not be distinguished from the nonlinear effects associated with propagation of sound through the surrounding fluid. In the second configuration, the interaction of ultrasound with bonded plates is considered. In the theoretical model, nonlinear effects are assumed to occur only at the bond. Particular attention is paid to changes in the reflection and transmission coefficients, as well as the second harmonic radiated from the plate, as a function of bond stiffness. Experiments were performed using bonded aluminum and acrylic plates. Measurements are in qualitative agreement with linear theory, but nonlinear effects at the bond were not observed. In the first two configurations, nonlinearity within the plate is taken into account, but not diffraction of the ultrasound beams. In the third configuration, the interaction of a sound beam with a plate at oblique incidence is examined. Here, beam diffraction is taken into account, but plate nonlinearity is considered to be negligible. The theoretical model is based on an angular spectrum method, and accounts for Lamb wave propagation within the plate. At Lamb excitation angles, nonspecular effects occur in the reflected and transmitted sound beams. Second harmonic generation is assumed to occur only in the fluid. Experiments were performed on an aluminum plate in water, and quantitative agreement is found between theory and measurements.