A mixed 3D-Shell analytical model for the prediction of sound transmission through sandwich cylinders

The sound transmission through an infinite multilayer cylinder composed of orthotropic skins and an isotropic polymer core is calculated analytically. The motions of the two thin orthotropic skins are described with the first-order shear deformation theory while the isotropic core is modeled with the three-dimensional elasticity theory. The polymer core transfer matrix relating the displacements and the stresses at the two common interfaces between the core and the skins is first 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 multilayer cylinder. The sound Transmission Loss (TL) of the cylinder excited by an acoustic plane wave is finally calculated. Our results are compared with results published recently in the literature. Excellent agreement is observed for thin cores where the three layers vibrate in phase in the radial direction. The usefulness of the three-dimensional model is demonstrated for a thick and soft core in the higher frequency domain where the skins are vibrating out of phase with a relative displacement in the radial direction. Finally, a parametric study is conducted to demonstrate the influence of the damping of each layer and some observations are made on the shear and compressional strain energies of each layer.