Sound radiation from a line forced perforated elastic sandwich panel

Abstract

Composite barriers, consisting of thin plates separated by light matrix structures, are widely used for fuselage construction in the aircraft industry, and in partitions in the building trade. The acoustical properties of such materials can vary considerably by altering the interior geometry, and perforations can be added to one or both sides. With perforations the interior cavities can act as Helmholtz resonators, causing a substantial modification to the overall transmission and reflection properties of such barriers. Leppington [Proc. R. Soc. London, Ser. A 427, 385–399 (1990)] devised an effective boundary condition for a perforated sandwich plate structure, valid in the limit of low frequency (acoustical waves long compared with the typical dimensions of the hole/cavity construction), and obtained transmission and reflection coefficients for infinite planar structures. This article investigates the radiation properties of perforated sandwich plates by examining a simple infinite one-dimensional model (employing Leppington’s effective boundary condition) which is loaded by a line force or moment. The radiated far field, and unattenuated subsonic plate wave coefficients, are found explicitly, and are plotted over a range of frequencies for two physical configurations, namely an aluminum plate in water and in air. It is revealed that, unlike the usual thin plate equation, the model discussed herein has two bi-directional unattenuated plate waves, and for the structure in air the two waves are of similar magnitude over most frequencies. Surprisingly, these amplitudes are shown to become very large at a frequency below that of the structure’s Helmholtz resonance frequency. Further, the field radiating into air is also significantly modified by the cavity/perforations well away from the Helmholtz frequency.