Finite difference modeling and slowness‐time analysis of modes in a submerged steel plate

Abstract

This presentation illustrates one of the capabilities of a numerical laboratory in the study of acoustic‐elastic wave interaction. Because of the simultaneous presence of many modes of vibration, multipath, and mode conversion, physical experiments are difficult to instrument well enough to unravel the wave interactions. As an alternative, numerical results from a 2‐D finite difference solution to the elastodynamic equations mimic the physical interaction of a transient acoustic pulse with a finite elastic object. In this case the field variables of velocity and stress are computed directly and instrumentation is not an issue. In the experiment presented here, a 500‐Hz center frequency pulse insonifies a submerged steel plate with dimensions ≈2λ × λ/20, where λ is the wavelength in steel. Diffractions from the ends of the plate are observed as well as the flexural and longitudinal plate modes that arise from the coupling of acoustic to elastic energy. In addition, radiation of acoustic energy into the water from the ends of the plate is seen when the flexural and longitudinal modes impact from the interior. A fundamental question of the scattering process is how much of the insonifying acoustic energy is converted into elastic energy in the plate. While the plate modes occur simultaneously and overlap in the time domain, they can be separated into isolated regions of the slowness‐time domain. The isolation of the modes in this domain enables estimates of the energy partitioning to be made. From a time series recorded just below the midline of the plate, a slowness spectrum clearly shows the flexural and longitudinal modes in isolation. In addition, the continual reflection of these modes from the ends of the plate, i.e., the multipath, is seen as they travel back and forth. Quantitative estimates of energy partitioning are possible from the slowness spectra.