Unveiling the physics of acoustic insulation: multilayer flow resistivity estimation

Abstract

This paper presents a computational methodology aimed at precisely estimating the physical law governing equivalent flow resistivity in multilayer rigid porous materials, with a specific focus on applications in acoustic insulation systems. While existing models are capable of predicting sound transmission through individual layers, they lack a direct theoretical analytical link between the flow resistivity of multilayer materials and the properties of their constituent layers. To address this gap, the study harnesses equivalent fluid theory, which integrates visco-inertial interactions between the material structure and the interstitial fluid. By establishing simplified expressions for the transmission coefficient of a bilayer medium under low-frequency Darcy conditions, the paper introduces a novel approach to estimation. Furthermore, it formulates a concise relationship between the resistivity of the bilayer medium and the resistivity and thickness of each layer, which extends to multilayer configurations. Experimental validation with bilayer samples demonstrates significant agreement between the directly obtained equivalent flux resistivity and the theoretically predicted values, with relative errors ranging from 3 to 18%. The significance of this paper lies in its practical implications for acoustic insulation systems, where accurate predictions of acoustic performance are crucial. The research introduces a reliable physical relationship for estimating the equivalent flow resistivity of a multilayer as a function of the flow resistivity of each constituent layer and its thickness, offering theoretical correlation with empirical data and providing an alternative to labor-intensive experimental methods and software. This contribution to acoustics facilitates accurate prediction and characterization of the acoustic properties of multilayer materials, thereby aiding in the design of effective noise control systems.