Wave propagation in viscoelastic phononic crystal rods with internal resonators

In the present work, the wave propagation in a viscoelastic phononic crystal rod with internal periodic dissipative resonators is investigated. The Kelvin-Voigt model is utilized to describe the viscoelastic behavior of host materials. The Bloch theorem is adopted to analyze the band structure of the rod. The effect of the free oscillation frequency of the resonators on the band structure is firstly studied. It is found that by tailoring the dynamic characteristics of the resonators, the coupling of the Bragg scattering (BS) and local resonance (LR) mechanisms can be harnessed to effectively widen the band gaps and enhance the wave attenuation. Then, the effects of the viscosity of the host materials and the damping of the resonators on the band structure, especially the two nearly coalescent band gaps (the first Bragg and LR ones), are investigated respectively. Furthermore, the combined effect of the two dissipative sources is also discussed. The present work is expected to be helpful to the design and applications of phononic crystals and metamaterials.