Study on band gap properties of two-dimensional phononic crystals based on generalized viscoelastic modeling

Abstract

Viscoelastic materials can dissipate energy and hinder propagation for plane waves, which can adjust the band structures of phononic crystals (PCs). In this study, the wave propagation in a two-dimensional PC with a viscoelastic matrix is investigated. The Maxwell model is utilized to analyze the effect of material parameters on the frequency dependence of viscoelasticity. Material parameters include the relaxation time, the initial value and the final value of the shear modulus. Band structures of viscoelastic phononic crystals (VPCs) are solved by combining the plane wave expansion method and iterative algorithm based on Bloch theory. The effects of the viscoelasticity on the band structures are studied using the single-mode and multi-mode Maxwell models. Results reveal that the viscoelasticity of the materials not only extends the band gaps but also shifts the band gaps to lower frequencies. Furthermore, the viscoelasticity simulated by the multi-mode model can precisely adjust anyone of the band gaps of VPCs separately. Results provide insights into the design and applications of VPCs.