Accuracy of Simple Approximations Used to Calculate Axially Symmetric Extensional Vibrations of Elastic Ring Transducer

Abstract

A complete mathematical model of a free-flooded ring transducer must predict the ring's surface velocity distri- bution when the forces acting on the ring are known. The acoustic radiation from a radially oscillating cylindrical ring is a function of its surface velocity distribution. In particular, the far-field radiation on the axis of the ring is a sensitive func- tion of the difference between the inside and outside surface areas and radial velocities and the axially directed edge veloc- ity. The theoretical determination of the velocity distribution of an unloaded elastic ring oscillating in its lowest order purely radial mode is performed by back of the envelope approxi- mations commonly used by transducer engineers and by a more sophisticated calculation based on the theory of Gustafsson and Kane for high-frequency extensional vibrations of a circular disk with a concentric hole. The results are com- pared and the transducer engineer can utilize this comparison to judge the confidence with which he may apply his easily ob- tained approximate results to the design of a free-flooded ring transducer with a specified velocity distribution.