Bandgap Structures of SH-Wave in a One-Dimensional Phononic Crystal with Viscoelastic Interfaces

Phononic crystal is an artificial periodic structure with the ability to regulate and control the wave propagation of particular frequencies and has been widely used in many applications. The adhesive layer bonding different constituents in the periodic structure of phononic crystals is usually a viscoelastic material, which has frequency-dependent material properties. In this paper, an analytical model based on the transfer matrix method is developed to study the bandgap structures of SH-wave (a shear wave with the propagation direction normal to the motion plane) in a one-dimensional phononic crystal consisting of two different elastic constituents bonded by the viscoelastic adhesive layer. The results show that the viscosity of the adhesive layer has a significant influence on the bandgap structure at the region of high frequency. The effects of various material parameters of the viscoelastic adhesive layer such as the relaxation time, the final-state modulus and the initial-state modulus are systematically studied. These results are very helpful in the practical design of phononic crystals involving the viscoelastic adhesive layers.