On the sound produced when flexural waves are reflected at the open end of a fluid-loaded elastic cylinder

Abstract

An analysis is made of the sound generated when an axisymmetric flexural wave is incident on the open end of a fluid-loaded, circular elastic cylinder. The flexural motions are assumed to be governed by the Donnell thin shell equations, and particular attention is given to the case of heavy fluid loading. Detailed predictions are made for the two extremes in which the edge of the open end is either (i) free to vibrate without restraint, or (ii) clamped. It is shown that, when the frequency ω exceeds the ring frequency ωr the efficiency with which sound is produced (i.e., the ratio of the scattered sound power to the incident wave power) is the same as for sound generated by a bending wave incident normally on the edge of a flat, elastic plate of the same thickness and edge condition. Below the ring frequency the efficiency is found to decrease like ω2 for a free edge, and to become negligible when ω≪ωr. When the edge is clamped, however, the low-frequency sound is radiated principally by a leaky extensional mode of the cylinder (coupled to the fluid via the influence of wall curvature), which is also produced by the edge interaction, and the acoustic efficiency tends to a constant value that depends on the fluid loading, and the material properties and radius of the cylinder, but is independent of frequency for ω≪ωr. Numerical results are given for a steel cylinder in water and (in less detail) in air.