Experimental investigation of the wave propagation on a point-driven, submerged capped cylinder using K-space analysis

Abstract

Classically, sparse accelerometer measurements are made on vibrating structures to help in deducing the physics of the vibration. However, the experimenter now has at his command more sophisticated measurement tools, such as nearfield acoustical holography or laser Doppler velocimetry, which provide much more data. Often complete mapping of the acceleration or displacements on the surface of these structures can be acquired. As a result, more sophisticated analysis tools must be developed. Such a tool useful for vibrating structures which are basically cylindrical or planar, is presented herein. The measured spatial velocity is decomposed at fixed temporal frequencies into its helical-wave spectrum, also known as the K-space spectrum. This decomposition contains a great deal of information about the physics of the vibrator. For example, it provides the dominant wavenumbers (the dispersion diagram) of free waves that exist on the shell. These free waves reach maximum amplitudes when close to a resonance frequency. The decomposition also provides an indication of the modal density of the shell. This technique is applied to experimental measurements on a shaker-driven, fluid-loaded, capped cylinder. The resulting helical wavenumber diagrams, plotted at a single frequency of excitation, show strong ‘‘figure 8’’ patterns. By comparison with helical-wave spectra computed from infinite-shell theory, it is shown that these patterns represent the wavenumber loci of the free waves that exist on the experimental shell. Excellent agreement between the measured helical-wave spectrum and predictions from infinite-shell theory are reported. The helical-wave spectra of the acoustic pressure, mapped on a cylindrical contour in the extreme nearfield of the capped cylinder, is also presented. From this spectra, the free waves on the structure can be identified and, in particular, how they participate in acoustic radiation. The frequency region was ka=0.5–2.0.