Finite amplitude effects in rectangular cavities with perturbed boundaries.

Abstract

The effects of boundary perturbations on finite-amplitude acoustical standing waves in rectangular, rigid-walled cavities were investigated using non-linear theory. When a high amplitude standing wave of frequency w is generated in a cavity, non-linear effects will cause a stimulation of certain normal modes whose resonance frequencies are integer multiples of w. Previous experimental observations revealed that there could be excitation of other normal modes, not belonging to the family of the driven mode, which v/as not predicted by the non-linear theory. The purpose of this research v/as to investigate the possibility that deviations from the idealized geometry could account for these observations. Of the various mechanisms possible, this work investigated the possibility of these unpredicted excitations occurring through a non-linear mechanism. The standing waves that exist in an ideal cavity must be corrected when the boundaries are irregular. The non-linear interaction between these standing waves and the corrections was studied. The ability of this interaction to excite standing waves other than those predicted in the ideal case was verified. A specific example was worked out demonstrating an unpredicted excitation, the strength of which was on the order of the magnitude of the boundary perturbation parameter.