On the Influence of Certain Geometric Characteristics of the Resonator on the Impedance Determined by the Dean’s Method

Abstract

This article considers the influence of the orifice arrangement in a cover of a cylindrical resonator on the impedance determined by the Dean’s method. A resonator with a small height and a low perforation degree is studied. This geometry provides different non-uniformity of the sound field at the resonator backing depending on the orifice arrangement in the resonator cover, while the number of orifices does not change. It is shown that, with different orifice arrangements, the impedance values determined by Dean’s method at high frequencies (3000 Hz and more) differ greatly. The authors propose the modification of Dean’s formula by using the amplitude coefficient of the zeroth order mode instead of the acoustic pressure at the resonator backing. The computations performed demonstrate that, in this case, the impedance does not depend on the orifice arrangement in the resonator cover. The computations consist of three stages: numerical simulation of the plane wave incidence onto the resonator (simulating a full-scale experiment); carrying out a modal analysis of the sound field at the resonator backing to extract the zeroth order mode; and determination of the resonator impedance according to the modified Dean’s formula.