Impulse responses and radiation impedances of cylindrical vibrators using wave-vector-time domain (k-t) methods

Abstract

A wave-vector-time domain (k-t) method is presented to evaluate the harmonic and time-dependent loading on a cylindrical shell that is vibrating with a specified spatial and time-dependent velocity. The method is based on utilizing a specified time-dependent modal expansion for the radial velocity of the vibrator. The acoustic loading on the vibrator is also expressed as a modal expansion in which each coefficient is a summation of convolution integrals of the modal velocity coefficients with mode-dependent radiation impulse responses. In contrast to an earlier work [D. D. Ebenezer and Peter R. Stepanishen, J. Acoust. Soc. Am. 81, 854–860 (1987)], the radiation impulse responses are evaluated using a (k-t) method based on a time-dependent Green's function for a baffled cylindrical vibrator. A comparison of the new method with the earlier method is presented along with numerical results for various axial mode shapes and circumferential mode numbers. [Work supported by ONR.]