Free Vibration of Thick Multi-Layer Viscoelastic Cylinders

The problem of the free vibration of thick multi-layered viscoelastic cylinders is studied and an analytical solution is presented. The three-dimensional theory of elasto-dynamics is used to develop the governing equation of motion. A mathematical approach linking modal displacements and stresses for each interface is utilized to determine a propagator matrix. Applying the appropriate boundary conditions, the propagator matrix can provide the natural frequencies and modal loss-factors for the multi-layered cylinder. It should be noted that the analysis is not limited to thin elastic shells, cylinders with any thickness can be considered. Several case studies are considered and comparisons are made with those reported for single elastic, laminated multi-layer cylinders and constrained rings. The effect of varying the core material loss-factor, and the effect of the outer layer thickness on the natural frequencies and their corresponding modal loss-factors for a three layered cylinder are studied. These results play an important role in optimizing the effectiveness of constrained layer damping treatment for design purposes