Multilayer cylinders are widely used in aeronautics and aerospace industries, in applications such as aircrafts, helicopters or space launch vehicles. Generally designed to be as light as possible, these structures must also take into account the problem of noise transmission inside passenger or payload compartments. Indeed, protection against noise is still necessary in such applications, whether it is for the comfort of passengers or for the protection of payloads. Thus, an optimization tool is necessary to reduce the total weight of the structure while increasing its acoustic efficiency. Consequently, fast analytical models have to be developed in order to predict accurately the sound transmission through these cylindrical structures.

In these applications, porous elastic materials are widely used to reduce the noise transmitted inside the interior compartment. Many studies have been made to model the behavior of these porous materials, and the literature reveals a large number of publications on this subject, with two approaches. The first approach is to model the porous media as an equivalent fluid. The viscous and thermal effects due to the skeleton are hence considered, but the skeleton elasticity is neglected. The second approach is to use the Biot's model. In this case, the motion of the skeleton is taken into account through the elasto-dynamic equations. This basic model considers the porous material as a superposition of two coupled solid and fluid phases. It is more adapted to model the dynamic behavior of porous elastic materials.

Sound transmission through multilayer structures with a porous elastic coating is a good example where the skeleton elasticity has an important effect. In the case of cylindrical structures, works have been published on sound transmission using equivalent fluid models. However, to our knowledge, no work has been published on the sound transmission through a cylindrical structure with a porous coating modeled with the Biot's theory.

In this study, a mixed "Biot-Shell" analytical model dedicated to the calculation of sound transmission through an infinite sandwich cylinder composed of orthotropic skins and a porous elastic core is presented. The motion of the two thin orthotropic skins is described with the first-order shear deformation theory while the porous elastic 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 porous elastic material. First, the global dynamic equilibrium of the sandwich structure is presented, and the Transmission Loss (TL) of the cylinder excited by an incident acoustic plane wave is calculated. Then, some numerical results obtained with the mixed analytical model are presented. The model is firstly validated by comparison with a finite element model, where excellent agreement is observed. The usefulness of Biot's model in this type of problem is then demonstrated by comparing the results with those obtained with equivalent fluid models. Finally, the mixed "Biot-Shell" analytical model is used to demonstrate the influence of the structural damping, and to study the sound transmission in different configurations.