Analytical coupled vibroacoustic modeling of membrane-coupled Helmholtz resonator

The membrane-coupled Helmholtz resonator (MCHR) offers distinct advantages for ultralow-frequency sound absorption. In this study, an analytical model of the MCHR is developed to investigate its vibroacoustic behavior under perpendicular acoustic incidence. The MCHR comprises a membrane backed by a shallow cavity and enclosed within a rigid frame containing multiple apertures. Governing equations are first derived based on membrane deformation and incompressible air motion in the aperture. Subsequently, a coupled membrane–Helmholtz model is then formulated by incorporating cavity-pressure variations induced by the relative motion between the membrane and the aperture air. The accuracy and applicability of the theoretical model are validated through comparison with finite element simulations. Furthermore, the influence of key parameters—including aperture radius and depth, as well as membrane elastic modulus and loss factor—on sound absorption performance is examined quantitatively. Results show that the first absorption peak arises primarily from Helmholtz resonance between the aperture and the cavity, whereas the second and third peaks are mainly due to energy dissipation in the aperture and the membrane, both resulting from membrane resonance. The established analytical model of the MCHR can thus serve as an effective tool for designing this class of membrane-type acoustic metamaterials.