Inhomogeneous plane-wave scattering and mode stimulation on periodic rough surfaces

Abstract

Medium vibration properties to characterize interface layers and quality of bonding can be examined by an ordinary approach using homogeneous waves or by a more general inhomogeneous (or complex harmonic) wave scattering technique. It is known that only particular inhomogeneous plane waves can stimulate eigenvibrations of a given structure, and not the homogeneous wave. The reflection and transmission of such inhomogeneous waves is investigated for plane parallel interfaces as well as their scattering at periodically corrugated boundaries between liquid and solids. The influence of plate thickness, corrugation periodicity, and height on the occurrence of specific plate modes is examined. Using an alternative description of a bounded ultrasonic beam as a finite superposition of inhomogeneous waves, this theory can be applied to examine the deformation of Gaussian profiles and to explicitly relate this deformation to the stimulation of mode vibrations. The generation of a plate—or interface—mode by an obliquely incident single inhomogeneous wave on a plane parallel plate—or half-space interface boundary—and the scattering of inhomogeneous waves at the interface wave stimulated corrugated surface, also suggest a new interpretation of back reflection and transmission of bounded beams at smooth liquid–solid interfaces.