Validation of a model on the coupling between circular membrane and Helmholtz resonator

Abstract

Recently, a model was proposed to describe the resonance characteristics of a modified Helmholtz resonator with a circular membrane fitted to one of the cavity walls. The model is based on two equations of motion: 1) One equation for the transverse wave formed on the membrane and 2) the second for the displacement of the air volume in the port of the Helmholtz resonator. When two equations were solved for the displacement of the membrane as a function of the radius, it was shown that, due to the coupling, the resonance frequencies would vary depending on the parameters of the Helmholtz resonator, which may be observed only for the modes with circular nodal lines. In the current study, the proposed model was further validated in a series of measurements under various conditions, and the results were discussed and compared to the predictions of previous models.