DMS-9500723 Harris This work investigates the propagation of surface waves over the curved elastic surfaces of a shell and studies how these waves couple from one surface to another. The curved shell is an elastic waveguide whose properties change slowly with wavelength, these changes being caused by the varying radii of curvature and thickness, while its two surfaces form weakly coupled surface-wave waveguides. The propagation is studied by asymptotically expanding the wavefields in inverse powers of the radii of curvature with each term subsequently expanded in the Rayleigh-Lamb modes. The beating over the propagation path of the two lowest Rayleigh-Lamb modes gives rise to a surface wave that couples back and forth between the two surfaces. The scattering that a surface wave experiences when it strikes a compact discontinuity near one of the surfaces or encounters a region of roughness along one of them is also studied. The compact scatterer is modeled by assigning it reflection and transmission coefficients determined from a local analysis of the wavefields near the discontinuity. The roughness is modeled by working out the attenuation to the surface wave. The results of this work will be compared to existing data at the Center for Nondestructive Evaluation at Iowa State University. Turbine blades rotated at high speeds and pipelines used to carry oil or natural gas are among the common curved structures ultrasonically inspected for damage such as fatigue cracking or corrosion. Fatigue cracks in a turbine blade often occur at its root, a location not always visually accessible. Corrosion to a pipeline can begin at its interior supface where it cannot be detected unless a section of the line is shut down. This work investigates how these curved, elastic shell structures can be inspected using surface waves that propagate first over the exterior surface, then over the interior surface, ultimately returning to the exterior surface where they are picked up. Th ese waves detect damage to an interior surface and carry that information to the exterior. Ultrasonic inspections must also give an estimate of the seriousness of the damage. By modeling scattering from a small surface crack or attenuation caused by a patch of corrosion, this work enables the information carried by a surface wave from one surface to another to be interpreted to give quantitative estimates of the damage.
