A mixed “Biot-Shell” analytical model for the prediction of sound transmission through a sandwich cylinder with a poroelastic core

A mixed “Biot-Shell” analytical model dedicated to the calculation of sound transmission through an infinite sandwich cylinder composed of orthotropic skins and a poroelastic core is proposed in this paper. The motion of the two thin orthotropic skins is described with the first-order shear deformation theory while the poroelastic core is modeled with the full 3D Biot׳s theory. The main advantage of this mixed model is that it takes into account the elasticity effects related to the skeleton of the poroelastic material. First, an analytical expression of the displacement and stress fields of the solid and fluid phases in the poroelastic layer is presented in cylindrical coordinates. Then, the poroelastic core transfer matrix relating the displacements and the stresses at the two common interfaces between the core and the skins is calculated. The coupling of the two skins is then made using the modal transfer matrix of the core, leading to the global dynamic equilibrium of the sandwich cylinder. The proposed model is finally used to calculate the sound Transmission Loss (TL) of infinite cylinders excited by an incident plane wave. Excellent agreement is observed in comparison with a finite element model. The usefulness of Biot׳s model in this type of problem is demonstrated by comparing the results with those obtained with equivalent fluid models. The mixed “Biot-Shell” analytical model is finally used to demonstrate the influence of the structural damping of each layer and to study the sound transmission in different configurations.