Evanescent surface acoustic waves in 1D viscoelastic phononic crystals

In this paper, evanescent surface waves propagating in a one-dimensional surface phononic crystal are investigated. The phononic crystal consists of elastic pillars periodically arranged on a viscoelastic substrate. By using the finite element method, the complex band structures and transmission spectra of surface waves are calculated. It is found that the evanescent wave with $π$ phase change of the real part lies inside the resonant bandgap, and no cusp is observed for the minimum imaginary part. With the increase of frequency, the surface waves can be gradually converted to bulk waves. When the pillar height is increased, the generation mechanism of the first bandgap gradually varies from Bragg scattering to local resonance, and the evanescent waves above the sound line can be reconstructed and shifted below the sound line. When the viscosity is introduced, the minimum imaginary part inside the bandgap decreases. However, the corresponding attenuation is strengthened because the contribution of the bulk wave to the transmission gets weak. The work in this paper is relevant to the practical application of surface waves.