Abstract
The behavior of guided flexural waves of an infinite, elastic, thick-walled circular cylinder immersed in fluid is considered in the low-frequency limit. The fluid is of lower density than the solid. The dependence of field quantities on φ, t, and x is of the form einφe−iωteikx, where n is the circumferential wave number, ω is the frequency of vibration, k is the wave number in the axial direction, φ is the circumferential coordinate, t is time, and x is the coordinate in the direction of the cylinder axis. Solutions for the exact dispersion relation based on the full elastodynamic equations will be presented. Appropriate approximations will be shown for a simplified representation of the dispersion relation of the lowest-order flexural wave. It will be shown that standard shell theory results correspond to different limits of the exact result. [Work supported by the PSU Applied Research Laboratory Exploratory and Foundational Research Program. The author acknowledges the advice of A. D. Pierce.]
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